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: $-4y$, second: $-9y$

Step2: Find constants to cancel y

To eliminate $y$, we need the coefficients of $y$ to be additive inverses. Multiply first equation by 9: $9(-4y) = -36y$. Multiply second equation by $-4$: $-4(-9y) = 36y$. Adding these gives $-36y + 36y = 0$.

Step3: Verify other options

• Option1: $3(-4y)=-12y$, $5(-9y)=-45y$ → sum is $-57y$ (no cancel)
• Option2: $3(-4y)=-12y$, $-5(-9y)=45y$ → sum is $33y$ (no cancel)
• Option3: $9(-4y)=-36y$, $4(-9y)=-36y$ → sum is $-72y$ (no cancel)

Answer:

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