Question

If $(x,y)$ is a solution to the system of equations $\{\begin{array}{c}4x+4y=14-y\\ x-5y=2\end{array}$
Then the value of $x-y$ is

• A. $\frac{1}{4}$
• B. $1$
• C. $3$
• D. $18$

Answer 1

The correct option is C $3$

Simplification of the first equation gives us $4x+4y=14$ or $x+y=\frac{7}{2}$...(i)

Consider the second equation $x-5y=2$....(ii)

Subtracting equation (ii) from (i) gives us $6y=\frac{3}{2}$ or $y=\frac{1}{4}$

Substituting it in equation (i) gives us $x=\frac{13}{4}$.
Hence, $x-y=\frac{13-1}{4}=\frac{12}{4}=3$