Sure, let's solve the given system of equations step-by-step using substitution.
The system of equations is:
[tex]\[
\begin{array}{l}
4x + 3y = 23 \\
x = 5y
\end{array}
\][/tex]
1. Start with the second equation [tex]\( x = 5y \)[/tex]:
This equation explicitly defines [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]. Now, we can substitute [tex]\( x = 5y \)[/tex] into the first equation.
2. Substitute [tex]\( x = 5y \)[/tex] into the first equation [tex]\( 4x + 3y = 23 \)[/tex]:
[tex]\[
4(5y) + 3y = 23
\][/tex]
3. Simplify the equation:
[tex]\[
20y + 3y = 23
\][/tex]
4. Combine like terms:
[tex]\[
23y = 23
\][/tex]
5. Solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{23}{23}
\][/tex]
[tex]\[
y = 1
\][/tex]
We have found that [tex]\( y = 1 \)[/tex].
6. Substitute [tex]\( y = 1 \)[/tex] back into the equation [tex]\( x = 5y \)[/tex] to find [tex]\( x \)[/tex]:
[tex]\[
x = 5(1)
\][/tex]
[tex]\[
x = 5
\][/tex]
So, the solution to the system of equations is:
[tex]\[
x = 5, \quad y = 1
\][/tex]
Therefore, the solution is [tex]\( (5, 1) \)[/tex].
