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.
