Question

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 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 9 and the second equation by -4.

Explanation:

Step1: Identify y coefficients

First equation y-coeff: $-4$; Second: $-9$

Step2: Find opposites for elimination

We need coefficients of y that are additive inverses. Multiply first eq by 9: $9*(-4)=-36$; multiply second eq by $-4$: $-4*(-9)=36$. $-36 + 36 = 0$, eliminating y.

Step3: Verify other options

Option 1: $3*(-4)=-12$, $5*(-9)=-45$; sum $-57≠0$. Option2: $3*(-4)=-12$, $-5*(-9)=45$; sum $33≠0$. Option3: $9*(-4)=-36$, $4*(-9)=-36$; sum $-72≠0$.

Answer:

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