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:
- \( 6x - 3y = 18 \)
- \( -3x - 9y = -93 \)
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.
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