Question

6x-3y=18 and -3x-9y=-93
In order to solve this system of equations using elimination/combination method, the first thing you should do is
Multiply the first equation by 3
Multiply the first equation by -2
Multiply the second equation by 2
Multiply the second equation by -3

Answer 1

To solve the system of equations using the elimination method, we want to manipulate the equations in such a way that adding or subtracting them eliminates one of the variables.

The system of equations is:
1. \( 6x - 3y = 18 \)
2. \( -3x - 9y = -93 \)

To facilitate elimination, we can focus on making the coefficients of either \( x \) or \( y \) equal (but opposite). Let's eliminate \( y \).

Looking at the coefficients of \( y \):
- The first equation has a coefficient of \(-3\) for \( y \).
- The second equation has a coefficient of \(-9\) for \( y \).

To make the coefficients equal in magnitude, we could multiply the first equation by \( 3 \), making the \( y \) term \(-9\) as well:

So, if we multiply the first equation \( 6x - 3y = 18 \) by \( 3 \), we get:
\[
18x - 9y = 54
\]

The second equation is already \( -3x - 9y = -93 \).

Now we can add these two equations to eliminate \( y \):
- New first equation: \( 18x - 9y = 54 \)
- Second equation: \( -3x - 9y = -93 \)

Thus, the correct choice is:
**Multiply the first equation by 3.**

This will allow us to eliminate \( y \) when we combine the two equations.