Consider the system of equations shown below to answer questions Question 21 and 22.

Question

(6x-3y=18
-3x-9y=-93)
Question 21
In order to solve this system of equations using the elimination/combination method, the first thing Emma should do is
*
1 point
A. multiply the first equation by 3
B. multiply the first equation by -2
C. multiply the second equation by 2
D. multiply the second equation by -3
Question 22
The value of the x will be
*
1 point
A. -3
B. 7
C. 8
D. 18

Answer 1

To solve the given system of equations:

1. \( 6x - 3y = 18 \)
2. \( -3x - 9y = -93 \)

Question 21 To use the elimination method, we can choose to eliminate one of the variables by creating coefficients that are opposites for either \(x\) or \(y\).

Let's eliminate \(y\). The first equation has a coefficient of \(-3\) for \(y\), and the second equation has \(-9\) for \(y\). We could multiply the first equation by 3, which will make the coefficient of \(y\) in the first equation \(-9\), matching the second equation.

Therefore, the correct answer is: A. multiply the first equation by 3

---

Question 22 Next, we will actually solve the system using the elimination method.

First, we'll multiply the first equation by 3:

\[ 3(6x - 3y) = 3(18) \] \[ 18x - 9y = 54 \]

Now our system of equations looks like:

1. \( 18x - 9y = 54 \)
2. \( -3x - 9y = -93 \)

Next, we can eliminate \(y\) by subtracting the second equation from the first:

\[ (18x - 9y) - (-3x - 9y) = 54 - (-93) \] \[ 18x - 9y + 3x + 9y = 54 + 93 \] \[ 21x = 147 \]

Now, we solve for \(x\):

\[ x = \frac{147}{21} = 7 \]

So, the value of \(x\) is: B. 7