1. Multiply the first equation by 3,and multiply the second equation by -2.
3(5x+2y=15)
−2(3x+3y=9)
Becomes:
15x+6y=45
−6x−6y=−18
Add these equations to eliminate y:
9x=27
Then solve 9x=27for x:
9x
/9
=
27
/9
(Divide both sides by 9)
x=3
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
5x+2y=15
Substitute3forxin5x+2y=15:
(5)(3)+2y=15
2y+15=15(Simplify both sides of the equation)
2y+15+−15=15+−15(Add -15 to both sides)
2y=0
2y
/2
=
0
/2
(Divide both sides by 2)
y=0
2. Multiply the second equation by -1, then add the equations together.
(4x+2y=−7)
−1(4x−6y=−11)
Becomes:
4x+2y=−7
−4x+6y=11
Add these equations to eliminate x:
8y=4
Then solve 8y=4 for y:
8y
/8
=4
/8
(Divide both sides by 8)
y= 1
/2
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
4x+2y=−7
Substitute
1
/2 for y in 4x+2y=−7:
4x+2(
1
/2
)=−7
4x+1=−7(Simplify both sides of the equation)
4x+1+−1=−7+−1(Add -1 to both sides)
4x=−8
4x
/4
=
−8
/4
(Divide both sides by 4)
x=−2
Answer:
x=−2 and y= 1/2
