Question

Solve the following pair of equations:

$13+2y=9x$, $3y=7x$

• A. $x=8;y=3$
• B. $x=0;y=5$
• C. $x=3;y=7$
• D. $x=1;y=9$

Answer 1

Answer: (C)

$x=3;y=7$

The equation $13+2y=9x$ can be written as $9x-2y=13$.Another equation $3y=7x$ can be written as $7x-3y=0$. Then we get the equations:

$9x-2y=\mathrm{13.........}\left(1\right)$

$7x-3y=\mathrm{0.........}\left(2\right)$

Multiply the equation 1 by $7$ and equation 2 by $9$ to make the coefficients of $x$ equal. Then we get the equations:

$63x-14y=\mathrm{91.........}\left(3\right)$

$63x-27y=\mathrm{0.........}\left(4\right)$

Subtract Equation 4 from equation 3 to eliminate $x$, because the coefficients of $x$ are the same. So, we get

$(63x-63x)+(-14y+27y)=91-0$

i.e. $13y=91$

i.e. $y=7$

Substituting this value of $y$ in equation 1, we get

$9x-14=13$

i.e. $9x=13+14=27$

i.e. $x=3$

Hence, the solution of the equations is $x=3,y=7$.