Question

Solve the following pairs of linear (simultaneous) equation by the method of elimination :$2x+3y=8$, $2x=2+3y$

• A. $x=2$, $y=\frac{3}{2}$
• B. $x=3$, $y=5$
• C. $x=\frac{5}{2}$, $y=1$
• D. $x=\frac{3}{2}$, $y=4$

Answer 1

The correct option is C $x=\frac{5}{2}$, $y=1$

The equation $2x=2+3y$ can be rewritten as $2x-3y=2$, therefore, the equations are:

$2x+3y=\mathrm{8.........}\left(1\right)$

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

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

$(2x-2x)+(3y+3y)=8-2$

i.e. $6y=6$

i.e. $y=1$

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

$2x=2+3$

i.e. $2x=5$

i.e. $x=\frac{5}{2}$

Hence, the solution of the equations is $x=\frac{5}{2},y=1$.