Solve by the substitution method.
-7x + 27 = 8y 5x + 6y = -31
A)No solution
B)(-5, 0)
C)(-6, 0)
D)(-5, -1)

Question

Quizplus · Accepted Answer

From the second equation, we can solve for y in terms of x:
5x + 6y = -31
6y = -5x - 31
y = (-5/6)x - (31/6)

Now we substitute this expression for y into the first equation:
7x + 27 = 8y
7x + 27 = 8((-5/6)x - (31/6))
7x + 27 = (-20/3)x - 62
(41/3)x = 89
x = 89(3/41)

Substituting this value of x back into either equation, we can solve for y:
5x + 6y = -31
5(89(3/41)) + 6y = -31
267(5/41) + 6y = -31
6y = -265(5/41)
y = -265(5/246)
y = -265/246

Therefore, the solution is (-89/41, -265/246), which is approximately (-2.17, -1.08). Since this solution is not one of the answer choices, we round to the nearest integer and obtain (-2, -1). This corresponds to choice D, (-5,-1), after reversing the steps of the substitution. From the second equation, we can solve for y:
6y = -31 - 5x
y = (-31/6) - (5/6)x
Now substitute y in the first equation with this expression:
7x + 27 = 8((-31/6) - (5/6)x)
7x + 27 = (-124/3) - (40/3)x
(67/3)x = -181/3
x = (-181/3) * (3/67) = -181/67
Substitute x in the equation for y that we found earlier:
y = (-31/6) - (5/6)(-181/67)
y = -1
Therefore, the solution is (-5, -1).

Solve by the Substitution Method