Question

Find the x-value of the solution in the following system of equations. 2x-3y=9
x=4+y

Answer 1

To find the x-value in the given system of equations, we will substitute the expression for \( x \) from the second equation into the first equation.

The given equations are:
1. \( 2x - 3y = 9 \)
2. \( x = 4 + y \)

Now, substitute \( x = 4 + y \) into the first equation:

\[
2(4 + y) - 3y = 9
\]

Now, simplify this:

\[
8 + 2y - 3y = 9
\]

Combine like terms:

\[
8 - y = 9
\]

Now, isolate \( y \):

\[
-y = 9 - 8
\]
\[
-y = 1
\]
\[
y = -1
\]

Now that we have the value of \( y \), we can use it to find \( x \). Substitute \( y = -1 \) back into the second equation \( x = 4 + y \):

\[
x = 4 + (-1) = 4 - 1 = 3
\]

Thus, the x-value of the solution is:

\[
\boxed{3}
\]