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Chapter 5: Q. 5.5 (page 616)

Solve the system by elimination.

4x+y=-5-2x-2y=-2

Short Answer

Expert verified

The solution of the given system is(x,y)=(-2,3).

Step by step solution

01

Step 1. Given information

The given system is4x+y=-5-2x-2y=-2

02

Step 2. Solve for x

4x+y=-5-2x-2y=-2Given2(4x+y=-5)鈬�8x+2y=-10Multiplyfirstequationby2-2x-2y=-2

Add both equations

8x+2y=-10-2x-2y=-26x=-12x=-126solveforxx=-2

03

Step 3. Solve for y

Substitutex=-2intofirstequation4x+y=-54(-2)+y=-5-8+y=-5y=-5+8y=3

Hence, the solution is(x,y)=(-2,3).

04

Step 4. Verify the solution

Substitute(x,y)=(-2,3) into given equations4x+y=-5鈬�4(-2)+3=-5-8+3=-5-5=-5true-2x-2y=-2鈬�-2(-2)-2(3)=-24-6=-2-2=-2true

Thus, both equations are true.

Hence, the solution is(-2,3).

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