High School Math 2012 Common-core Algebra 1 Practice And Problem        Solvingworkbook Grade 8/9
High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
1st Edition
ISBN: 9780133185614
Author: Prentice Hall
Publisher: Prentice Hall
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Textbook Question
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Chapter 6.1, Problem 8P

Solve each system by graphing. Check your solution.

y = 4 3 x 3

y = 2 3 x + 3

Expert Solution & Answer
Check Mark
To determine

To Graph: Solve the system of equations to find value of x and y using graphing method and check the solution.

Answer to Problem 8P

The value of x=3 and y=1 .

Explanation of Solution

Given information: y=43x3 --------(1)

and y=23x+3 -------(2)

Graph:

Graph the system of equations using slope and y-intercept method.

For equation (1)

  y=43x3

Slope =43 and y intercept =3

To graph the line, firstly represent the y intercept (0,-3) and using slope = =riserun find the rise and run.

  Rise=4

  Run=3

From y intercept (0,-3) move up 4 units and right 3 units to get another point.

Then join the points and extend the line on both ends.

For equation (2)

  y=23x+3

Slope =23 and y intercept =3

Now, represent the y intercept (0,3) on the xy plane and find another point using slope using formula RiseRun .

  Rise=2Run=3

From y intercept move down 2 units and right 3 units to get next point. Then join the points and extend the line on both ends.

The graph of the given linear equations are

  High School Math 2012 Common-core Algebra 1 Practice And Problem        Solvingworkbook Grade 8/9, Chapter 6.1, Problem 8P

Interpretation: The red line represents the graph of equation (1) and the Blue line represents graph of equation (2). The lines intersect at (3,1). So, the solution to the system of equations is (3,1).

Check:

Plug in x as 3 and y as 1 into each equation to check whether the equation is true or not.

For equation (1)

  1=43(3)3

Simplify the right side of the equation

  1=43

  1=1

Yes! The equation is true. So, the (3,1) is solution to the equation (1)

Now for equation (2)

  1=23(3)+3

  1=2+3

  1=1

Yes! The equation is true for the solution set (3,1). So this is solution to the equation (2)

So, the (3,1) is solution to the both equations.

Chapter 6 Solutions

High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9

Ch. 6.1 - Reasoning If the graphs of the equations in a...Ch. 6.1 - Writing Explain the method used to graph a line...Ch. 6.1 - Reasoning If the ordered pair (3,2) satisfies one...Ch. 6.1 - Writing If the graphs of two lines in a system do...Ch. 6.1 - Reasoning Without graphing, decide whether the...Ch. 6.1 - Five years from now, a fathers age will be three...Ch. 6.1 - The denominator of a fraction is greater than its...Ch. 6.1 - The sum of the distances two hikers walked is 53...Ch. 6.1 - The result of dividing a two-digit number by the...Ch. 6.1 - Solve each system by graphing. Tell whether the...Ch. 6.1 - Solve each system by graphing. Tell whether the...Ch. 6.1 - Solve each system by graphing. Tell whether the...Ch. 6.1 - Solve each system by graphing. Tell whether the...Ch. 6.1 - Solve each system by graphing. Tell whether the...Ch. 6.1 - Solve each system by graphing. Tell whether the...Ch. 6.1 - Solve each system by graphing. Tell whether the...Ch. 6.1 - Solve each system by graphing. Tell whether the...Ch. 6.1 - Solve each system by graphing. Tell whether the...Ch. 6.1 - Solve each system by graphing. Tell whether the...Ch. 6.1 - Solve each system by graphing. Tell whether the...Ch. 6.1 - Solve each system by graphing. Tell whether the...Ch. 6.1 - The measure of one of the angles of a triangle is...Ch. 6.1 - For Exercises 14, choose the correct letter. Which...Ch. 6.1 - For Exercises 14, choose the correct letter. How...Ch. 6.1 - For Exercises 14, choose the correct letter. What...Ch. 6.1 - For Exercises 14, choose the correct letter. Which...Ch. 6.1 - For Exercises 1-4, choose the correct letter. A...Ch. 6.2 - Solve each system by substitution. Check your...Ch. 6.2 - Solve each system by substitution. Check your...Ch. 6.2 - Solve each system by substitution. Check your...Ch. 6.2 - Solve each system by substitution. Check your...Ch. 6.2 - Solve each system by substitution. Check your...Ch. 6.2 - Solve each system by substitution. Check your...Ch. 6.2 - Solve each system by substitution. Check your...Ch. 6.2 - Solve each system by substitution. Check your...Ch. 6.2 - Solve each system by substitution. Check your...Ch. 6.2 - Writing How do you know that substitution gives...Ch. 6.2 - Reasoning With the substitution method, which...Ch. 6.2 - Writing How can you use substitution method to...Ch. 6.2 - 6y+2x=3 Writing When solving the system of...Ch. 6.2 - Reasoning Can you tell that there is no solution...Ch. 6.2 - If the difference in the side lengths of two...Ch. 6.2 - A shopper purchased 8 T-Shirts and 5 pairs pants...Ch. 6.2 - A student bought 1 box of crayons and 5 reams of...Ch. 6.2 - Suppose you got 8 mangoes and 3 apples for $18 and...Ch. 6.2 - A shopper purchased 4 tables and 2 chairs for $200...Ch. 6.2 - If the length of the rectangle is twice the width,...Ch. 6.2 - The population of a city is 2,500. If the number...Ch. 6.2 - Solve each system by substitution. Tell whether...Ch. 6.2 - Solve each system by substitution. Tell whether...Ch. 6.2 - Solve each system by substitution. Tell whether...Ch. 6.2 - Solve each system by substitution. Tell whether...Ch. 6.2 - Solve each system by substitution. Tell whether...Ch. 6.2 - Solve each system by substitution. Tell whether...Ch. 6.2 - Solve each system by substitution. Tell whether...Ch. 6.2 - Solve each system by substitution. Tell whether...Ch. 6.2 - Solve each system by substitution. Tell whether...Ch. 6.2 - Solve each system by substitution. Tell whether...Ch. 6.2 - Solve each system by substitution. Tell whether...Ch. 6.2 - Solve each system by substitution. Tell whether...Ch. 6.2 - Solve each exercise and enter your answer on the...Ch. 6.2 - Solve each exercise and enter your answer on the...Ch. 6.2 - Solve each exercise and enter your answer on the...Ch. 6.2 - Solve each exercise and enter your answer on the...Ch. 6.2 - Solve each exercise and enter your answer on the...Ch. 6.3 - Solve each system using elimination. x+y=2 xy=4Ch. 6.3 - Solve each system using elimination. x+2y=3 xy=6Ch. 6.3 - Solve each system using elimination. 2xy=4 3xy=2Ch. 6.3 - Solve each system using elimination. x2y=2 x+y=3Ch. 6.3 - Solve each system using elimination. x3y=3 2x+3y=5Ch. 6.3 - Solve each system using elimination. x+2y=4 x+y=2Ch. 6.3 - Solve each system using elimination. 3x2y=8 2x2y=5Ch. 6.3 - Solve each system using elimination. x2y=3 3xy=2Ch. 6.3 - Solve each system using elimination. 2x4y=6 xy=1Ch. 6.3 - 3x5y=9 Writing For the system 2x+y=3 which...Ch. 6.3 - Open-Ended If you do not have equal coefficients...Ch. 6.3 - In a class, 45 students take the SAT exam. The...Ch. 6.3 - Open-Ended Write a system for which using the...Ch. 6.3 - Error Analysis A student solved a system of linear...Ch. 6.3 - A farm raises a total of 220 chickens and pigs....Ch. 6.3 - You drive a car that runs on ethanol and gas. You...Ch. 6.3 - Your math test has 38 questions and is worth 200...Ch. 6.3 - A student bought 3 boxes of pencils and 2 boxes of...Ch. 6.3 - Solve each system using elimination. Tell whether...Ch. 6.3 - Solve each system using elimination. Tell whether...Ch. 6.3 - Solve each system using elimination. Tell whether...Ch. 6.3 - Solve each system using elimination. Tell whether...Ch. 6.3 - Solve each system using elimination. Tell whether...Ch. 6.3 - Solve each system using elimination. Tell whether...Ch. 6.3 - Solve each system using elimination. Tell whether...Ch. 6.3 - Solve each system using elimination. Tell whether...Ch. 6.3 - Solve each system using elimination. Tell whether...Ch. 6.3 - Solve each system using elimination. Tell whether...Ch. 6.3 - Solve each system using elimination. Tell whether...Ch. 6.3 - Solve each system using elimination. Tell whether...Ch. 6.3 - How is the multiplication or division property of...Ch. 6.3 - For Exercises 15, choose the correct letter. What...Ch. 6.3 - For Exercises 15, choose the correct letter. The...Ch. 6.3 - For Exercises 15, choose the correct letter. What...Ch. 6.3 - For Exercises 15, choose the correct letter. Two...Ch. 6.3 - For Exercises 15, choose the correct letter. What...Ch. 6.3 - A hotel is offering the two weekend specials...Ch. 6.4 - Solve each word problem You have $6000 to invest...Ch. 6.4 - Solve each word problem During a sale at the local...Ch. 6.4 - Solve each word problem The sum of two numbers is...Ch. 6.4 - Solve each word problem One plane at 520 feet is...Ch. 6.4 - Solve each word problem The perimeter of a...Ch. 6.4 - Solve each word problem You are getting ready to...Ch. 6.4 - Solve each word problem You have a cable plan that...Ch. 6.4 - Solve each word problem At an all-you-can-eat...Ch. 6.4 - Solve each system. Explain why you chose the...Ch. 6.4 - Solve each system. Explain why you chose the...Ch. 6.4 - Solve each system. Explain why you chose the...Ch. 6.4 - Solve each system. Explain why you chose the...Ch. 6.4 - Solve each system. Explain why you chose the...Ch. 6.4 - Solve each system. Explain why you chose the...Ch. 6.4 - Open-Ended What are three differences between an...Ch. 6.4 - Reasoning One number is 4 less than 3 times a...Ch. 6.4 - Error Analysis In Exercise 16, what kind of errors...Ch. 6.4 - A plane leaves Chicago and flies 750 miles to New...Ch. 6.4 - A coin bank has 250 coins, dimes and quarters,...Ch. 6.4 - In 4 years, a mother will be 5 times as old as her...Ch. 6.4 - For Exercises 15, choose the correct letter. You...Ch. 6.4 - For Exercises 15, choose the correct letter. The...Ch. 6.4 - For Exercises 15, choose the correct letter. You...Ch. 6.4 - For Exercises 15, choose the correct letter....Ch. 6.4 - For Exercises 15, choose the correct letter. A...Ch. 6.4 - Rectangle EFGH has a perimeter of 24 inches, and...Ch. 6.5 - Graph each linear inequality. x4Ch. 6.5 - Graph each linear inequality. y2Ch. 6.5 - Graph each linear inequality. 3xy6Ch. 6.5 - Graph each linear inequality. 4x+5y3Ch. 6.5 - Graph each linear inequality. 3x+2y6Ch. 6.5 - Graph each linear inequality. yxCh. 6.5 - Graph each linear inequality. 3x5y6Ch. 6.5 - Graph each linear inequality. x44y3Ch. 6.5 - Graph each linear inequality. x44y3Ch. 6.5 - Error Analysis A student graphed y4x+3 as shown....Ch. 6.5 - Writing How do you decide which half-plane to...Ch. 6.5 - Determine whether the ordered pair is a solution...Ch. 6.5 - Determine whether the ordered pair is a solution...Ch. 6.5 - Determine whether the ordered pair is a solution...Ch. 6.5 - Determine whether the ordered pair is a solution...Ch. 6.5 - Determine whether the ordered pair is a solution...Ch. 6.5 - Determine whether the ordered pair is a solution...Ch. 6.5 - Determine whether the ordered pair is a solution...Ch. 6.5 - Determine whether the ordered pair is a solution...Ch. 6.5 - Write an inequality that represents each graph.Ch. 6.5 - Write an inequality that represents each graph.Ch. 6.5 - You and some friends have $30. You want to order...Ch. 6.5 - Tickets to a play cost $5 at the door and $4 in...Ch. 6.5 - Reasoning Two students did a problem as above, but...Ch. 6.5 - For Exercises 15, choose the correct letter. What...Ch. 6.5 - For Exercises 15, choose the correct letter. For...Ch. 6.5 - For Exercises 15, choose the correct letter. If x0...Ch. 6.5 - For Exercises 15, choose the correct letter. Which...Ch. 6.5 - For Exercises 15, choose the correct letter. How...Ch. 6.5 - A school fundraiser sells holiday cards and...Ch. 6.6 - Solve each system of inequalities by graphing....Ch. 6.6 - Solve each system of inequalities by graphing....Ch. 6.6 - Solve each system of inequalities by graphing....Ch. 6.6 - Writing What is the difference between the...Ch. 6.6 - Open-Ended When can you say that there is no...Ch. 6.6 - Error Analysis A student graphs the system below....Ch. 6.6 - Determine whether the ordered pair is a solution...Ch. 6.6 - Determine whether the ordered pair is a solution...Ch. 6.6 - Determine whether the ordered pair is a solution...Ch. 6.6 - Mark is a student, and he can work for at most 20...Ch. 6.6 - Britney wants to bake at most 10 loaves of bread...Ch. 6.6 - Write a system of inequalities for the following...Ch. 6.6 - Solve each system of inequalities by graphing....Ch. 6.6 - Solve each system of inequalities by graphing....Ch. 6.6 - Solve each system of inequalities by graphing....Ch. 6.6 - For Exercises 14, choose the correct letter. You...Ch. 6.6 - Which of the following systems of inequalities...Ch. 6.6 - For the graph above, what is the approximate...Ch. 6.6 - A student spends no more than 2 hours on his math...Ch. 6.6 - A young woman wants to make at least $200 a week...
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