Question

5.
Find a solution to the following system of equations.
−5x + y = −5
−4x + 2y = 2


(–8, –15)


(0, 1)


(2, 5)


(–2, –15)

Answer 1

To find a solution to the given system of equations, we can use either the substitution method or the elimination method. Let's use the elimination method to solve the system of equations:

\[
\begin{cases}
-5x + y = -5 & \quad(1) \\
-4x + 2y = 2 & \quad(2)
\end{cases}
\]

First, we want to eliminate one of the variables. Let's eliminate \( y \). To do this, we first manipulate equation (1) so that one of the coefficients of \( y \) in both equations is the same.

Equation (1) is already given as:
\[
-5x + y = -5
\]

Multiply equation (1) by 2 to match the coefficient of \( y \) in equation (2):
\[
2(-5x + y) = 2(-5)
\]

This simplifies to:
\[
-10x + 2y = -10 \quad(3)
\]

Now we have the system:
\[
\begin{cases}
-10x + 2y = -10 & \quad(3) \\
-4x + 2y = 2 & \quad(2)
\end{cases}
\]

Subtract equation (2) from equation (3) to eliminate \( y \):
\[
(-10x + 2y) - (-4x + 2y) = -10 - 2
\]

This simplifies to:
\[
-10x + 2y + 4x - 2y = -12
\]
\[
-6x = -12
\]
\[
x = 2
\]

Now that we have \( x = 2 \), we substitute \( x \) back into one of the original equations to find \( y \). Let's use equation (1):
\[
-5(2) + y = -5
\]
\[
-10 + y = -5
\]
\[
y = -5 + 10
\]
\[
y = 5
\]

So, the solution to the system of equations is \( (x, y) = (2, 5) \).

Therefore, the correct answer is \( (2, 5) \).