Question

Part 1. How many solutions will the following system of linear equations have?

Answer 1

In part 1, we are given with two equations and according to the degrees of freedom rule, two equations should solve two unknowns. The number of solutions is a pair of two variables. Hence the answer is B
In part 2, this is just a matter of substitution or in a long way solve each expressions for their x and y. The answer should be D. 
In part 3, we can use a calculator to solve the system of equations. Using addition to eliminate y, too, the answer is C.

Answer 2

–2x + 4y = –7 . . . . . (1)
y = -1/2x + 5 . . . . . . (2)
Putting (2) into (1), we have:
-2x + 4(-1/2x + 5) = -7
-2x - 2x + 5 = -7
-4x = -7 - 5 = -12
x = -12/-4 = 3
y = -1/2(3) + 5 = -3/2 + 5 = 7/2
Hence, the system has one solution.