Question

Solve the system by substitution.
y, equals, 5, x
y=
5x
y, equals, 7, x, minus, 16
y=
7x−16

Answer 1

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

1. \( y = 5x \)
2. \( y = 7x - 16 \)

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

\[
5x = 7x - 16
\]

Next, we will solve for \( x \). Subtract \( 5x \) from both sides:

\[
0 = 7x - 5x - 16
\]

This simplifies to:

\[
0 = 2x - 16
\]

Now, add 16 to both sides:

\[
16 = 2x
\]

Next, divide both sides by 2:

\[
x = 8
\]

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

\[
y = 5x = 5(8) = 40
\]

So, the solution to the system of equations is:

\[
(x, y) = (8, 40)
\]

To verify, we can substitute \( x = 8 \) into the second equation:

\[
y = 7(8) - 16 = 56 - 16 = 40
\]

Both equations yield \( y = 40 \), confirming our solution is valid.

Thus, the solution to the system is:

\[
\boxed{(8, 40)}
\]