Question

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

Consider the system of equations above. If $(x,y)$ is the solution to the system, then what is the value of $y$?

• A. $\frac{2}{21}$
• B. $\frac{30}{7}$
• C. $\frac{15}{2}$
• D. $Noneoftheabove$

Answer 1

The correct option is B $\frac{30}{7}$

Put value of $y$ in second equation $\frac{2}{3}x=\frac{4}{7}x+\frac{5}{7}$
$\frac{2}{3}x-\frac{4}{7}x=\frac{5}{7}$
$\frac{14x-12x}{21}=\frac{5}{7}$
$\frac{2}{21}x=\frac{5}{7}$
$x=\left(\frac{21}{2}\right)\times \frac{5}{7}$
$x=\frac{15}{2}$
Now that we know $x$, we can find the value of $y$ using the first equation $y=\frac{4}{7}x$
$=\frac{4}{7}\times \frac{15}{2}$
$=\frac{60}{14}=\frac{30}{7}$
The solution to the equation is $(x,y)=(\frac{15}{2},\frac{30}{7})$. The answer we want is the value of $y$, which is $\frac{30}{7}$