Question

Solve the following pairs of linear (simultaneous) equation by the method of elimination : $2x-3y=7$, $5x+y=9$

• A. $x=2$ and $y=-1$
• B. $x=4$ and $y=0$
• C. $x=-3$ and $y=-5$
• D. $x=-7$ and $y=6$

Answer 1

The correct option is A $x=2$ and $y=-1$

Multiply the equation $2x-3y=7$ by $5$ and equation $5x+y=9$ by $2$ to make the coefficients of $x$ equal. Then we get the equations:

$10x-15y=\mathrm{35.........}\left(1\right)$

$10x+2y=\mathrm{18.........}\left(2\right)$

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

$(10x-10x)+(-15y-2y)=35-18$

i.e. $-17y=17$

i.e. $y=-1$

Substituting this value of $y$ in the equation $2x-3y=7$, we get

$2x+3=7$

i.e. $2x=4$

i.e. $x=2$

Hence, the solution of the equations is $x=2,y=-1$.