10
QuizMultiple Choice

Solving Systems of Linear Equations: Linear Combinations

Question 10 • GA-Algebra: Concepts and Connections CR

To eliminate the y-terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?First Equation: 5x − 4y = 28Second equation: 3x - 9y = 30

Answer
A
The first equation should be multiplied by 3 and the second equation by 5.
B
The first equation should be multiplied by 3 and the second equation by −5.
C
The first equation should be multiplied by 9 and the second equation by 4.
D
The first equation should be multiplied by 9 and the second equation by −4.

Explanation

The y-coefficients are −4 and −9, whose least common multiple in magnitude is 36. Multiply the first equation by 9 to get −36y, and the second equation by −4 to get +36y. When you add the equations, the y-terms cancel, so choice D is correct.

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