Question

Solve the following simultaneous equations by the method of equating coefficients.$\frac{x}{3}+5y=13;2x+\frac{y}{2}=19$

• A. $x=1,y=2$
• B. $x=9,y=2$
• C. $x=4,y=2$
• D. $x=8,y=2$

Answer 1

The correct option is B $x=9,y=2$

$\frac{x}{3}+5y=13$ ....(i)

$2x+\frac{y}{2}=19$ .....(ii)

Multiplying equation (i) by $3$ and equation (ii) by $2$. we get,

$x+15y=39$ ......(iii)

$4x+y=38$ ......(iv)

To make the coefficients of x equal multiplying equation (iii) by $4$. we get ,

$4x+60y=156$ .....(v)

Subtract equation (iii) from equation (iv). we get,

$4x+60y-(4x+y)=156-38$

$59y=118\Rightarrow y=2$

Substitute $y=2$ in equation (iii). we get,

$x+15\left(2\right)=39\Rightarrow x=9$

$\therefore x=9,y=2$