Solve Systems of Linear Equations 4

This question is for the redesigned SAT, which is for you, if you are taking the SAT in March 2016 and beyond.

Solving systems of linear equations with no solution

Question:

1/2x - 1/4y = 5
ax - 3y = 20

In the system of linear equations above, a is a constant. If the system has no solution, what is the value of a?

A) 1/2
B) 2
C) 6
D) 12

calculator usage: No calculator

Solution:

A system of equations has no solutions when the two equations form parallel lines, that is, when their slopes are equal and their y-intercepts are different.
Rewrite the two equations in the form y = mx + b.

1/2x - 1/4y = 5
1/4 y = 1/2 x - 5
y = 2x - 20

ax - 3y = 20
3y = ax - 20
y = a/3 x - 20/3

Equate the two slopes:
a/3 = 2
a = 6
The answer is C) 6

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