   Chapter 4.1, Problem 13E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 7-20, find all solutions of the given system of equations, and check your answer graphically.[HINT: See Examples 2-5.][HINT: In Exercises 13-16, first eliminate all fractions and decimals; see Example 3.] 0.5 x + 0.1 y = 0.7 0.2 x − 0.2 y = 0.6

To determine

To calculate: The solution to the system of equations 0.5x+0.1y=0.7 and 0.2x0.2y=0.6. and check the answer graphically.

Explanation

Given Information:

The provided system of equations is,

0.5x+0.1y=0.7 0.2x0.2y=0.6

Formula used:

Elimination Method:

This method is used to find the solutions of the system of linear equations by eliminating one of the two variables from the equations.

Multiply the equations with suitable non-zero numbers. Then combine the equations in such way so that one of the variables get eliminated and then evaluate the value of the other variable. Then substitute the value of this variable in either of the equations to get the value of the first variable.

To find the solution of a system of linear equations whose coefficients are either fractions or decimals, multiply the equations with suitable numbers to remove the fractions and decimals. Then solve the modified equations using elimination method.

Calculation:

Consider the equations,

0.5x+0.1y=0.7

...... (1)

0.2x0.2y=0.6

...... (2)

Multiply equation (1) by 10 to get rid of decimals.

10(0.5x+0.1y)=10(0.7)10(0.5x)+10(0.1y)=10(0.7)10(510)x+10(110)y=10(710)5x+y=7

...... (3)

Multiply equation (2) by 10 to get rid of decimals.

10(0.2x0.2y)=10(0.6)10(0.2x)10(0.2y)=10(0.6)10(210x)10(210y)=10(610)2x2y=6

...... (4)

To solve the modified equations (3) and (4), use elimination method.

Multiply equation (3) by 2 and equation (4) by 1.

2(5x+y)=(7)10x+2y=14

And

1(2x2y)=1(6)2x2y=6

Add equations 10x+2y=14 and 2x2y=6 to eliminate the variable y.

10x+2y=14 2x2y=6_       12x=20

Then evaluate the value of the variable x.

12x=20x=2012x=53

Substitute x=53 in the equation 5x+y=7 and evaluate the value of the variable y.

5(53)+y=7253+y=7y=7253y=21253

Simplify it further,

y=43

Then to find the solution of the modified system of equations, graphically, plot the graphs of the equations and find the intersection point

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