Use elimination to solve the system of equations:
{2x+3y=1
{x+4y=-2
show work

2x+3y=1;x+4y=−2

Steps:

Multiply the second equation by -2, then add the equations together.

(2x+3y=1)

−2(x+4y=−2)

Becomes:

2x+3y=1

−2x−8y=4

Add these equations to eliminate x:

−5y=5

Then solve−5y=5for y:

−5y−5=5−5(Divide both sides by -5)

y=−1

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

2x+3y=1

Substitute−1foryin2x+3y=1:

2x+(3)(−1)=1

2x−3=1(Simplify both sides of the equation)

2x−3+3=1+3(Add 3 to both sides)

2x=4

2x2=42(Divide both sides by 2)

x=2



x=2 and y=−1