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Chapter 5: Q. 344 (page 679)

In the following exercises, solve the systems of equations by substitution.

y=-2x+7y=23x-1

Short Answer

Expert verified

The solution set is(3,1).

Step by step solution

01

Step 1. Given Information

The given system of equations isy=-2x+7y=23x-1.

02

Step 2. Find the value of x.

  • Substitutey=-2x+7 into the second given equation.

-2x+7=23x-123x+2x=7+183x=8x=3

  • The value ofxis 3.
03

Step 3. Find the value of y.

  • Substitute x=3into the first given equation.

y=-2(3)+7=-6+7=1

  • So, the solution set is(3,1).
04

Step 4. Check the solution

  • Substitute x=3,y=1into both the given equations and check if the equations are satisfied.

1=?-2(3)+71=?-6+71=11=?23(3)-11=?2-11=1

  • As both the equations are satisfied, the solution is verified.

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