Solving with Elimination Quick Check

Question

1 of 51 of 5 Items
Question
Solve the system of two linear equations.
−3x−4y=−23

3x−5y=5
(1 point)
Responses

(5, 2)
left parenthesis 5 comma 2 right parenthesis

(−5, 2)
left parenthesis negative 5 comma 2 right parenthesis

(5,−2)
left parenthesis 5 comma negative 2 right parenthesis

(−5,−2)

Answer 1

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

1. \(-3x - 4y = -23\) (Equation 1)
2. \(3x - 5y = 5\) (Equation 2)

We can eliminate \(x\) by adding Equation 1 and Equation 2 together. First, we can rewrite Equation 1 for elimination:

Multiply Equation 2 by 1 (to keep it unchanged):

(Equation 1) \(-3x - 4y = -23\) (Equation 2) \(3x - 5y = 5\)

Now, add both equations:

\[ (-3x - 4y) + (3x - 5y) = -23 + 5 \]

This results in:

\[ (-4y - 5y) = -18 \] \[ -9y = -18 \]

Now, divide by \(-9\):

\[ y = 2 \]

Now that we have the value of \(y\), we can substitute it back into one of the original equations to find \(x\). Let's use Equation 2:

\[ 3x - 5(2) = 5 \]

This simplifies to:

\[ 3x - 10 = 5 \]

Adding 10 to both sides gives:

\[ 3x = 15 \]

Dividing by 3 yields:

\[ x = 5 \]

Thus, the solution to the system of equations is \((5, 2)\).

The correct response is:

\((5, 2)\)