Question

Solve the system of equations by substitution.

x + y = A system of equations. StartFraction 3 over 8 EndFraction x plus StartFraction one-third EndFraction y equals StartFractions 17 over 24 EndFraction.

x + 7y = 8

(
,
)

Answer 1

Interpret the system as
(3/8)x + (1/3)y = 17/24
x + 7y = 8.

From the second equation x = 8 − 7y. Substitute into the first:
(3/8)(8 − 7y) + (1/3)y = 17/24
3 − (21/8)y + (1/3)y = 17/24
Combine y-terms: −21/8 + 1/3 = −55/24, so
3 − (55/24)y = 17/24
−(55/24)y = 17/24 − 72/24 = −55/24
y = 1.

Then x = 8 − 7(1) = 1.

Solution: (1, 1).