Certainly! Let's solve the system of equations using the substitution method. The given system of equations is:
[tex]\[
\begin{cases}
3x + 4y = 9 \\
y = 2 - x
\end{cases}
\][/tex]
First, we'll substitute the second equation, [tex]\( y = 2 - x \)[/tex], into the first equation.
1. Substitute [tex]\( y = 2 - x \)[/tex] into [tex]\( 3x + 4y = 9 \)[/tex]:
[tex]\[
3x + 4(2 - x) = 9
\][/tex]
2. Distribute the 4 in the equation:
[tex]\[
3x + 8 - 4x = 9
\][/tex]
3. Combine like terms:
[tex]\[
3x - 4x + 8 = 9 \\
-x + 8 = 9
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
-x = 9 - 8 \\
-x = 1 \\
x = -1
\][/tex]
Now that we have [tex]\( x = -1 \)[/tex], we substitute this value back into the second equation to find [tex]\( y \)[/tex]:
5. Substitute [tex]\( x = -1 \)[/tex] into [tex]\( y = 2 - x \)[/tex]:
[tex]\[
y = 2 - (-1) \\
y = 2 + 1 \\
y = 3
\][/tex]
So, the solution to the system of equations is:
[tex]\[
(x, y) = (-1, 3)
\][/tex]
