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Solve Systems of Linear Equations 4

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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


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


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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