Respuesta :
STEPS USING SUBSTITUTION
5x−2y=17
2x−3y=9
To 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.
5x−2y=17,2x−3y=9
Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
5x−2y=17
Add 2y to both sides of the equation.
5x=2y+17
Divide both sides by 5.
x=
5
1
(2y+17)
Multiply
5
1
times 2y+17.
x=
5
2
y+
5
17
Substitute
5
2y+17
for x in the other equation, 2x−3y=9.
2(
5
2
y+
5
17
)−3y=9
Multiply 2 times
5
2y+17
.
5
4
y+
5
34
−3y=9
Add
5
4y
to −3y.
−
5
11
y+
5
34
=9
Subtract
5
34
from both sides of the equation.
−
5
11
y=
5
11
Divide both sides of the equation by −
5
11
, which is the same as multiplying both sides by the reciprocal of the fraction.
y=−1
Substitute −1 for y in x=
5
2
y+
5
17
. Because the resulting equation contains only one variable, you can solve for x directly.
x=
5
2
(−1)+
5
17
Multiply
5
2
times −1.
x=
5
−2+17
Add
5 /17
to −
5 /2
by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
x=3
The system is now solved.
x=3,y=−1
