a.
To write first step of elimination.
a.
Answer to Problem 6.3.1P
Explanation of Solution
Given information:
The first step of elimination is to make the coefficients of both equations equal.
For example, in given equation,
The coefficient of y is same, but if they were not, multiply both sides, of equation whose coefficient is to be equalled.
b.
To find the solution
b.
Answer to Problem 6.3.1P
Explanation of Solution
Given information:
Calculation Let Equation 1 be
Let Equation 2 be
To solve equations by elimination, the given equations are either added or subtracted to get an equation in only one variable.
Let’s eliminate variable x here. To eliminate a variable, the coefficients of the variable must be same in both the equations.
In equation 1, coefficient of x is 0.4 & in equation 2, coefficient of x is 0.8. To make the coefficients same, lets multiply equation 1 with 2.
This gives-
Now, subtracting equation 2 & equation 1’.
In the next step, x is eliminated-
Hence,
So,
Put value in (3)
Solving,
So,
Dividing by 0.8,
Hence,
c.
To graph the equation
c.
Explanation of Solution
Given:
Graph:
The blue line represents: 0. 4x - 2y=6
The black line represents: 0. 8x + 2y =0
Interpretation:
The intersection point of the line is (-2, 5) which also the solution of the system
of equation. Hence, the solution is correct.
d.
To find solution if line changed
d.
Answer to Problem 6.3.1P
Explanation of Solution
Given:
Line changed is
Calculation:
Now the lines are:
So, to solve equations by elimination, the given equations are either added or subtracted to get an equation in only one variable.
Let’s eliminate variable x here. To eliminate a variable, the coefficients of the variable must be same in both the equations.
In equation 1, coefficient of x is 0.4 & in equation 2, coefficient of x is 1 To make the coefficients same, lets divide equation 1 with 0.4.
Solving,
Subtracting equations,
In the next step, x is eliminated.
Hence,
Put in (3)
Solving,
Hence,
x =0
Chapter ISG Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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