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Chapter 5: Q. 5.54 (page 618)

Solve the system by elimination.

3x+2y=26x+5y=8

Short Answer

Expert verified

The solution of the system is(x,y)=(-2,4).

Step by step solution

01

Step 1.Given information

The given system is3x+2y=26x+5y=8

02

Step 2. Solve for y

3x+2y=26x+5y=8Given-2(3x+2y=2)鈬�-6x-4y=-4Multiplythefirstequationwith-26x+5y=8

Add both equations

-6x-4y=-46x+5y=8y=4

03

Step 3. Solve for x

3x+2y=2Firstequation3x+2(4)=2Substitutey=43x+8=2Solveforx3x=2-83x=-6x=-63x=-2

Hence, the solution is (x,y)=(-2,4).

04

Step 4. Verify the solution

3x+2y=2鈬�3(-2)+2(4)=2-6+8=22=2true6x+5y=8鈬�6(-2)+5(4)=8-12+20=88=8true

Both equations are true.

Hence, the solution is(x,y)=(-2,4).

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