Question

Solve the following pair of simultaneous equations:

$5x-6y=8$
$7y-15x=9$

• A. (1 , 3)
• B. (6 , -1)
• C. (-2 , -3)
• D. (3 , -5)

Answer 1

Answer: (C)

(-2 , -3)

Multiply the equation $5x-6y=8$ by $3$ to make the coefficients of $x$ equal.Another equation is $7y-15x=9$ or $-15x+7y=9$. Then we get the equations:

$15x-18y=\mathrm{24.........}\left(1\right)$

$-15x+7y=\mathrm{9.........}\left(2\right)$

Add Equations 1 and 2 to eliminate $x$, because the coefficients of $x$ are the same. So, we get

$(15x-15x)+(-18y+7y)=24+9$

i.e. $-11y=33$

i.e. $y=-3$

Substituting this value of $y$ in the equation $5x-6y=8$, we get

$5x+18=8$

i.e. $5x=-10$

i.e. $x=-2$

Hence, the solution of the equations is $x=-2,y=-3$.