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Sagot :
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.
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.
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