Solve the system of equations by either the addition method or the substitution method.?

Question

{(x + 5) / ( 2) = (y + 17) / ( 4)

{(x / 4) = (2y + 8) / (8)

a. (3, -1)
b. (-1, 3)
c. infinite number of solutions
d. no solution

Answer 1

first get rid of fractions by multiplying by the common denominator:

(x+5)/2 = (y+17)/4 becomes
2(x+5) = y + 17
2x + 10 = y + 17
2x - y = 7

x/4 = (2y+8)/8 becomes
2x = 2y + 8

at this point, substitute 2y+8 for 2x in the 1st equation:
2y + 8 - y = 7
y = -1

and then 2x = 2(-1) + 8
2x = 6, x = 3
so answer a.

Answer 2

2x + 10 = y + 17
2x = y + 7
2x = 2y + 8
y+7 = 2y + 8
y = -1
2x = -1 + 7 = 6
x = 3
ans is a.