Question

Solve the system by substitution.
y, equals, 2, x, minus, 14
y=
2x−14
y, equals, minus, 5, x
y=
−5x
Answer
Attempt 1 out of 2

Answer 1

To solve the system of equations by substitution, we have the following equations:

1. \( y = 2x - 14 \)
2. \( y = -5x \)

Since both equations equal \( y \), we can set them equal to each other:

\[
2x - 14 = -5x
\]

Now, let's solve for \( x \):

1. Add \( 5x \) to both sides:

\[
2x + 5x - 14 = 0
\]

This simplifies to:

\[
7x - 14 = 0
\]

2. Add 14 to both sides:

\[
7x = 14
\]

3. Divide by 7:

\[
x = 2
\]

Now that we have \( x \), we can substitute it back into either equation to find \( y \). Let's use the first equation:

\[
y = 2(2) - 14
\]
\[
y = 4 - 14
\]
\[
y = -10
\]

So the solution to the system of equations is:

\[
(x, y) = (2, -10)
\]

You can check the solution by substituting \( x = 2 \) into the second equation:

\[
y = -5(2) = -10
\]

This confirms our solution is correct. The final answer is:

\[
(x, y) = (2, -10)
\]