Question

Solve the following pair of simultaneous equations:

$4x-3y=8$
$3x-4y=-1$

• A. $x=3,y=-1$
• B. $x=5,y=4$
• C. $x=-4,y=2$
• D. $x=7,y=-6$

Answer 1

The correct option is B $x=5,y=4$

Multiply the equation $4x-3y=8$ by $3$ and equation $3x-4y=-1$ by $4$ to make the coefficients of $x$ equal. Then we get the equations:

$12x-9y=\mathrm{24.........}\left(1\right)$

$12x-16y=-\mathrm{4.........}\left(2\right)$

Subtract Equation (2) from Equation (1) to eliminate $x$, because the coefficients of $x$ are the same. So, we get

$(12x-12x)+(-9y+16y)=24+4$

i.e. $7y=28$

i.e. $y=4$

Substituting this value of $y$ in the equation $4x-3y=8$, we get

$4x-12=8$

i.e. $4x=20$

i.e. $x=5$

Hence, the solution of the equations is $x=5,y=4$.