Solving System of Equations for y
To solve the given system of equations for \( y \), follow these steps:
The system of equations given are:
\[ y = \frac{4}{7}x \]
\[ \frac{2}{3}x = y + \frac{5}{7} \]
First, we can use the first equation to substitute \( x \) in terms of \( y \) in the second equation. To find \( x \) in terms of \( y \) from the first equation, we rearrange the equation as:
\[ y = \frac{4}{7}x \]
\[ x = \frac{7}{4}y \]
Now we substitute \( x \) into the second equation:
\[ \frac{2}{3}\left(\frac{7}{4}y\right) = y + \frac{5}{7} \]
To solve for \( y \), we now multiply the terms:
\[ \frac{14}{12}y = y + \frac{5}{7} \]
Simplify the left side by reducing the fraction:
\[ \frac{7}{6}y = y + \frac{5}{7} \]
To solve for y, get all the terms involving y on one side of the equation:
\[ \frac{7}{6}y - y = \frac{5}{7} \]
Since \( y \) is the same as \( \frac{6}{6}y \), we can rewrite the equation as:
\[ \frac{7}{6}y - \frac{6}{6}y = \frac{5}{7} \]
Combine the y terms:
\[ \frac{1}{6}y = \frac{5}{7} \]
Finally, solve for \( y \) by multiplying both sides by the reciprocal of \( \frac{1}{6} \), which is 6:
\[ y = \frac{5}{7} \times 6 \]
\[ y = \frac{5 \times 6}{7} \]
\[ y = \frac{30}{7} \]
So the value of \( y \) is \( \frac{30}{7} \).
The correct answer is 30/7.
