Question

Solve using substitution.
y = 9x + 4
y = 10x + 5
(_,_)

Answer 1

To solve the system of equations using substitution, we have:

1. \( y = 9x + 4 \)
2. \( y = 10x + 5 \)

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

\[
9x + 4 = 10x + 5
\]

Now, we will solve for \( x \):

1. Subtract \( 9x \) from both sides:
\[
4 = 10x - 9x + 5
\]
This simplifies to:
\[
4 = x + 5
\]

2. Subtract 5 from both sides:
\[
4 - 5 = x
\]
So,
\[
x = -1
\]

Next, substitute \( x = -1 \) back into one of the original equations to find \( y \). We'll use the first equation:

\[
y = 9(-1) + 4
\]
\[
y = -9 + 4
\]
\[
y = -5
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-1, -5)
\]

Therefore, the final answer is:

\[
(-1, -5)
\]