Question

solving systems of linear equations: linear combinations
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 = 28
second equation: 3x - 9y = 30
the first equation should be multiplied by 3 and the second equation by 5.
the first equation should be multiplied by 9 and the second equation by 4.
the first equation should be multiplied by 3 and the second equation by -5.
the first equation should be multiplied by 9 and the second equation by -4.

Explanation:

Step1: Identify y-coefficients

First equation y-coefficient: $-4$, Second: $-9$

Step2: Find LCM of 4 and 9: $36$

Step3: Determine multipliers for 36

First equation: $\frac{36}{4}=9$ (or $-9$), Second: $\frac{36}{9}=4$ (or $-4$)

Step4: Check sign for elimination

We want $y$-terms to cancel. Multiply first by $9$ (makes $-36y$), second by $-4$ (makes $+36y$). $-36y + 36y = 0$.

Answer:

The first equation should be multiplied by 9 and the second equation by $-4$.