Certainly! Let's solve the given system of equations using substitution.
The given system is:
[tex]\[
\begin{aligned}
-4x + 3y &= 3 \quad \text{(1)} \\
y &= 3x - 4 \quad \text{(2)}
\end{aligned}
\][/tex]
Step 1: Solve one of the equations for one variable.
Equation (2) is already solved for [tex]\( y \)[/tex]:
[tex]\[ y = 3x - 4 \][/tex]
Step 2: Substitute this expression for [tex]\( y \)[/tex] into the other equation.
Substitute [tex]\( y = 3x - 4 \)[/tex] into Equation (1):
[tex]\[
-4x + 3(3x - 4) = 3
\][/tex]
Step 3: Simplify and solve for [tex]\( x \)[/tex].
Distribute the 3:
[tex]\[
-4x + 9x - 12 = 3
\][/tex]
Combine the [tex]\( x \)[/tex]-terms:
[tex]\[
5x - 12 = 3
\][/tex]
Add 12 to both sides:
[tex]\[
5x = 15
\][/tex]
Divide both sides by 5:
[tex]\[
x = 3
\][/tex]
Step 4: Substitute the value of [tex]\( x \)[/tex] back into the expression for [tex]\( y \)[/tex].
Substitute [tex]\( x = 3 \)[/tex] into [tex]\( y = 3x - 4 \)[/tex]:
[tex]\[
y = 3(3) - 4
\][/tex]
Simplify:
[tex]\[
y = 9 - 4
\][/tex]
[tex]\[
y = 5
\][/tex]
Final Solution:
[tex]\[
\begin{array}{l}
x = 3 \\
y = 5
\end{array}
\][/tex]
So the solution to the system of equations is [tex]\( x = 3 \)[/tex] and [tex]\( y = 5 \)[/tex].
