Question

Solve the following simultaneous equations by the method of equating coefficients.$\frac{x}{2}+3y=11;x+5y=20$

• A. $x=20,y=2$
• B. $x=15,y=2$
• C. $x=5,y=2$
• D. $x=10,y=2$

Answer 1

Answer: (D)

$x=10,y=2$

$\frac{x}{2}+3y=11\Rightarrow x+6y=22$ ....(i)

$x+5y=20$ .......(ii)

Since, coefficients of $x$ in both equations are equal.

On subtracting (ii) from (i). we get,

$x+6y-(x+5y)=22-20$

$\Rightarrow x+6y-x-5y=2$

$\Rightarrow y=2$

Substitute the value of $y=2$ in equation (i). we get,

$x+6\left(2\right)=22$

$\Rightarrow x=10$

$\therefore x=10,y=2$