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Solve the system by elimination.

3x+y=52x-3y=7

Short Answer

Expert verified

The solution of the given system is(x,y)=(2,-1).

Step by step solution

01

Step 1. Given information

The given system is3x+y=52x-3y=7.

02

Step 2. Solve for x

3x+y=52x-3y=7Given3(3x+y=5)=9x+3y=152x-3y=7Multiplyfirstequationby3

Add both equations

9x+3y=152x-3y=711x=22x=2211Solveforxx=2

03

Step 3. Solve for y

Substitute x=2in the first equation

3x+y=53(2)+y=56+y=5y=5-6y=-1

Hence, the solution isx,y=(2,-1).

04

Step 4.Verify the solution

Substitute (2,-1)into the given system of equations

3x+y=5⇒3(2)-1=5⇒6-1=5⇒5=5True2x-3y=7⇒2(2)-3(-1)=7⇒4+3=7⇒7=7True

Thus, both equations are true.

Hence, the solution is(2,-1).

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