Problem: solve by substitution 3x+2y=3 9x-8y=-2
use the substitution method to solve
1) 3x + 2y = 3
2) 9x - 8y = -2
Start by solving equation 1 for y in terms of x.
3x + 2y = 3
3x + 2y - 3x = 3 - 3x
2y = 3 - 3x
2y/2 = (3 - 3x)/2
y = 1.5 - 1.5x
Substitute that into equation 2.
9x - 8y = -2
9x - 8(1.5 - 1.5x) = -2
9x - 12 + 12x = -2
21x - 12 = -2
21x - 12 + 12 = -2 + 12
21x = 10
21x/21 = 10/21
x = 10/21
We use that in equation 1 to solve for y.
3x + 2y = 3
3(10/21) + 2y = 3
10/7 + 2y = 3
10/7 + 2y - 10/7 = 3 - 10/7
2y = 3 - 10/7
2y = 21/7 - 10/7
2y = 11/7
2y/2 = (11/7)/2
y = 11/14
Before we accept those values, check them in with
equation 2.
9x - 8y = -2
9(10/21) - 8(11/14) = -2
90/21 - 88/14 = -2
Let's change those fractions to a common denominator.
42 will do.
(90/21)(2/2) - (88/14)(3/3) = -2
180/42 - 264/42 = -2
-84/42 = -2
-2 = -2
The check verifies our numbers.
Answer: x = 10/21, y = 11/14