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

6x-5y=-12x+y=13

Short Answer

Expert verified

The solution of the system is(x,y)=(4,5).

Step by step solution

01

Step 1. Given information

The given system is6x-5y=-12x+y=13

02

Step 2. solve for x

6x-5y=-12x+y=13Given6x-5y=-15(2x+y)=5(13)Multiplyonbothsideswith56x-5y=-110x+5y=65Simplify

Add both equations

6x-5y=-110x+5y=6516x=64x=6416x=4

03

Step 3. solve for y

6x-5y=-1firstequation6(4)-5y=-1usex=424-5y=-1solvefory5y=24+15y=25y=255y=5

04

Step 4. Verify the solution

6x-5y=-1⇒6(4)-5(5)=-124-25=-1-1=-1true2x+y=13⇒2(4)+5=138+5=1313=13true

Both equations are true.

Hence, the solution is(x,y)=(4,5).

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