Solve the following system by the substitution method Check

Solve the following system by the substitution method. Check the solution(s). 3y - 5x = 44 x- 8y = -68 Select the correct choice below and, if necessary, fill in the answer box to complete your answer. The System has a single solution. The solution set is. (Simplify your answer Type an ordered pair) There are infinitely many solutions The solution set is {(x, y)|x - 8y = -68}. The solution set is the empty set

Solution

3y - 5x = 44 -------------(1)

x - 8y = -68 ------------(2)

Solving equation (2) for x.

x-8y =-68

Adding 8y on both sides

x -8y +8y = -68 +8y

x= 8y - 68

Substituting x= 8y - 68 in (1) equation

3y - 5(8y-68) = 44

Distributing -5 over (8y-68)

3y - 40y + 340 = 44

-37y + 340 = 44

Subtracting 340 from both sides

-37y +340 - 340 = 44- 340

-37y = -296

Dividing both sides by -37

-37y /-37 = -296 /-37

y= 8

Plugging y=8 in second equation x = 8y - 68

x= 8y -68 = 8(8) -68

= 64-68 = -4

x = -4

Therefore, System has a single solution. The solution set is {-4, 8}.