Part 1. how many solutions will the following system of linear equations have?
–2x + 4y = –7
y = -1/2x + 5
a.) 0
b.) 1
c.) 2
d.) infinite
part 2. for which system of equations is (5, 3) the solution?
a.) 3x – 2y = 9
3x + 2y = 14
b.) x – y = –2
4x – 3y = 11
c.) –2x – y = –13
x + 2y = –11
d.) 2x – y = 7
2x + 7y = 31
part 3. solve the system of equations.
8x – 3y = 1
–2x + 3y = 11
a.) (–1, –3)
b.) (–1, 3)
c.) (2, 5)
d.) (5, 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.

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.

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