x=5
y=−4To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
3x+4y=−1,−2x−5y=10
Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
3x+4y=−1
Subtract 4y from both sides of the equation.
3x=−4y−1
Divide both sides by 3.
x=
3
1
(−4y−1)
Multiply
3
1
times −4y−1.
x=−
3
4
y−
3
1
Substitute
3
−4y−1
for x in the other equation, −2x−5y=10.
−2(−
3
4
y−
3
1
)−5y=10
Multiply −2 times
3
−4y−1
.
3
8
y+
3
2
−5y=10
Add
3
8y
to −5y.
−
3
7
y+
3
2
=10
Subtract
3
2
from both sides of the equation.
−
3
7
y=
3
28
Divide both sides of the equation by −
3
7
, which is the same as multiplying both sides by the reciprocal of the fraction.
y=−4
Substitute −4 for y in x=−
3
4
y−
3
1
. Because the resulting equation contains only one variable, you can solve for x directly.
x=−
3
4
(−4)−
3
1
Multiply −
3
4
times −4.
x=
3
16−1
Add −
3
1
to
3
16
by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
x=5
The system is now solved.
x=5,y=−4