Systems of Linear Equations Online Practice

Question

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9 of 139 of 13 Items

Question
Solve the system.
−5x+4y=48

−5x−8y=24
(1 point)
Responses

(24,−18)
left parenthesis 24 comma negative 18 right parenthesis

(8, 2)
left parenthesis 8 comma 2 right parenthesis

(−24,−18)
left parenthesis negative 24 comma negative 18 right parenthesis

(−8, 2)

Answer 1

To solve the system of equations:

1. \( -5x + 4y = 48 \)
2. \( -5x - 8y = 24 \)

We can use substitution or elimination. Here, I'll use elimination.

First, we can eliminate \( -5x \) from both equations.

We can do this by subtracting the first equation from the second:

\[ (-5x - 8y) - (-5x + 4y) = 24 - 48 \]

This simplifies to:

\[ -8y - 4y = -24 \] \[ -12y = -24 \] \[ y = 2 \]

Now that we have \( y = 2 \), we can substitute this value back into one of the original equations to solve for \( x \). We'll use the first equation:

\[ -5x + 4(2) = 48 \] \[ -5x + 8 = 48 \] \[ -5x = 48 - 8 \] \[ -5x = 40 \] \[ x = -8 \]

Thus, the solution to the system of equations is \( (x, y) = (-8, 2) \).

The final answer is: \[ \boxed{(-8, 2)} \]