Certainly! To solve the system of equations by substitution, follow these steps:
Given the system of equations:
[tex]\[
\begin{array}{c}
\left\{
\begin{array}{l}
3x + 4y = 4 \\
2x + y = -9
\end{array}
\right.
\end{array}
\][/tex]
1. Solve the second equation for [tex]\( y \)[/tex]:
[tex]\[
2x + y = -9
\][/tex]
Rearrange it to express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[
y = -9 - 2x
\][/tex]
2. Substitute [tex]\( y = -9 - 2x \)[/tex] into the first equation [tex]\( 3x + 4y = 4 \)[/tex]:
[tex]\[
3x + 4(-9 - 2x) = 4
\][/tex]
3. Simplify and solve for [tex]\( x \)[/tex]:
[tex]\[
3x + 4(-9 - 2x) = 4 \\
3x - 36 - 8x = 4 \\
3x - 8x - 36 = 4 \\
-5x - 36 = 4 \\
-5x = 4 + 36 \\
-5x = 40 \\
x = \frac{40}{-5} \\
x = -8
\][/tex]
4. Substitute [tex]\( x = -8 \)[/tex] back into the expression for [tex]\( y \)[/tex]:
[tex]\[
y = -9 - 2(-8) \\
y = -9 + 16 \\
y = 7
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
(x, y) = (-8, 7)
\][/tex]
This provides the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations:
[tex]\[
\boxed{(-8, 7)}
\][/tex]
