Solving Simultaneous Equations Using Elimination Quick Check

Question

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Question
Solve the following system of equations using the elimination method.

3x−4y=−4, x+3y=−10

(1 point)
Responses

(−16,2)
left parenthesis negative 16 comma 2 right parenthesis

(−2,−4)
left parenthesis negative 2 comma negative 4 right parenthesis

(−16,−2)
left parenthesis negative 16 comma negative 2 right parenthesis

(−4,−2)
left parenthesis negative 4 comma negative 2 right parenthesis
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Answer 1

To solve the system of equations using the elimination method, we have the following two equations:

1. \( 3x - 4y = -4 \) (Equation 1)
2. \( x + 3y = -10 \) (Equation 2)

We can start by eliminating one of the variables. Let's eliminate \( x \). To do this, we can multiply Equation 2 by 3 so that the coefficients of \( x \) in both equations will be the same.

Multiply Equation 2 by 3:

\[ 3(x + 3y) = 3(-10) \]

This gives:

\[ 3x + 9y = -30 \quad \text{(Equation 3)} \]

Now we can set Equation 1 and Equation 3 up for elimination:

1. \( 3x - 4y = -4 \) (Equation 1)
2. \( 3x + 9y = -30 \) (Equation 3)

Next, we subtract Equation 1 from Equation 3:

\[ (3x + 9y) - (3x - 4y) = -30 - (-4) \]

This simplifies to:

\[ 9y + 4y = -30 + 4 \]

\[ 13y = -26 \]

Now, divide by 13:

\[ y = -2 \]

Now that we have \( y \), we can substitute it back into Equation 2 to solve for \( x \):

\[ x + 3y = -10 \]

Substituting \( y = -2 \):

\[ x + 3(-2) = -10 \]

\[ x - 6 = -10 \]

Adding 6 to both sides:

\[ x = -4 \]

The solution to the system of equations is \( (x, y) = (-4, -2) \).

So the correct answer is:

(−4,−2)