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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

**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

Go to next Question

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Heart of Algebra

More Lessons for SAT Math

More Resources for SAT

Algebra Tutorials

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

Go to next Question

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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