To solve the equation [tex]\( 5x + 7y = 35 \)[/tex] for [tex]\( y \)[/tex], let’s follow these steps:
1. Isolate the term containing [tex]\( y \)[/tex] on one side of the equation:
Start with the original equation:
[tex]\[
5x + 7y = 35
\][/tex]
2. Subtract [tex]\( 5x \)[/tex] from both sides of the equation to isolate [tex]\( y \)[/tex]-term:
[tex]\[
7y = 35 - 5x
\][/tex]
3. Divide every term by 7 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{35 - 5x}{7}
\][/tex]
4. Simplify the expression:
Divide both terms in the numerator by 7:
[tex]\[
y = \frac{35}{7} - \frac{5x}{7}
\][/tex]
[tex]\[
y = 5 - \frac{5x}{7}
\][/tex]
Therefore, the solution to the equation [tex]\( 5x + 7y = 35 \)[/tex] for [tex]\( y \)[/tex] is:
[tex]\[
y = 5 - \frac{5x}{7}
\][/tex]
Comparing this result with the given options:
A. [tex]\( y = \frac{5}{7} x - 5 \)[/tex]
B. [tex]\( y = 35 - 5 x \)[/tex]
C. [tex]\( y = 5 - \frac{5}{7} x \)[/tex]
D. [tex]\( y = 7 - \frac{7}{5} x \)[/tex]
The correct answer is:
[tex]\[
\boxed{y = 5 - \frac{5}{7} x}
\][/tex] which corresponds to option C.
