Solve using the substitution method.

Question

Show your work. -8x ? 4y = -68, x + 3y = 16

Answer 1

4y = -68
divide each side by 4
y = -68/4 = -17

substitute y = -17 in x + 3y = 16
x + 3 * -17 = 16
x - 51 = 16

Add 51 to each side
x = 16 + 51 = 67

now, -8x = -8 * 67 = -536

Answer 2

Substitution method :

Considering the equations as - 8x + 4y = - 68 and x + 3y = 16.

Simplify equation 2 : x + 3y = 16.

x = 16 - 3y.

Substitute x = 16 - 3y in equation 1 : - 8x + 4y = - 68.

- 8(16 - 3y) + 4y = - 68

Divide each side by 4.

- 2(16 - 3y) + y = - 17

- 32 + 6y + y = - 17

7y = - 17 + 32

7y = 15

⇒ y = 15/7.

Substitute the value y = 15/7 in either of equations (1) or (2) for x.

Equation 2 : x + 3y = 16.

x + 3(15/7) = 16

x = 16 - 45/7

x = (112 - 45)/7

⇒ x = 67/7.

The solution is (x, y) = (67/7, 15/7).