Enter the correct answer in the box.

Consider this system of equations:

[tex]\[
\begin{array}{l}
3x + 2y = 23 \\
\frac{1}{2}x - y = 4
\end{array}
\][/tex]

Rewrite the first equation in slope-intercept form to find an expression that can be substituted into the second equation.



Answer :

To rewrite the first equation [tex]\(3x + 2y = 23\)[/tex] in slope-intercept form and find an expression for [tex]\(y\)[/tex] that can be substituted into the second equation, we follow these steps:

1. Start with the first equation:
[tex]\[ 3x + 2y = 23 \][/tex]

2. To isolate [tex]\(y\)[/tex], we need to solve for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex]:
[tex]\[ 2y = 23 - 3x \][/tex]

3. Now, divide every term by 2 to solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{23}{2} - \frac{3x}{2} \][/tex]

Thus, the rewritten first equation in slope-intercept form is:
[tex]\[ y = \frac{23}{2} - \frac{3x}{2} \][/tex]

This expression for [tex]\(y\)[/tex] can now be substituted into the second equation if needed.