Question

$y = \frac{4}{7}x$
$
\frac{2}{3}x = y + \frac{5}{7}$
consider the system of equations. if $(x, y)$ is the solution to the system, then what is the value of $y$
choose 1 answer:
a $\frac{2}{21}$
b $\frac{30}{7}$
c $\frac{15}{2}$
d none of the above

Explanation:

Step1: Substitute $y$ into second equation

Substitute $y=\frac{4}{7}x$ into $\frac{2}{3}x = y + \frac{5}{7}$:
$\frac{2}{3}x = \frac{4}{7}x + \frac{5}{7}$

Step2: Isolate $x$ terms

Subtract $\frac{4}{7}x$ from both sides:
$\frac{2}{3}x - \frac{4}{7}x = \frac{5}{7}$
Find common denominator 21:
$\frac{14}{21}x - \frac{12}{21}x = \frac{5}{7}$
$\frac{2}{21}x = \frac{5}{7}$

Step3: Solve for $x$

Multiply both sides by $\frac{21}{2}$:
$x = \frac{5}{7} \times \frac{21}{2} = \frac{15}{2}$

Step4: Solve for $y$

Substitute $x=\frac{15}{2}$ into $y=\frac{4}{7}x$:
$y = \frac{4}{7} \times \frac{15}{2} = \frac{30}{7}$

Answer:

B. $\frac{30}{7}$