Question

If $(x,y)$ is a solution to the system $\{\begin{array}{c}-2x+5y=1\\ 7x-10y=-11\end{array}$, then the sum of $x$ and $y$ is

• A. $-\frac{137}{30}$
• B. $-4$
• C. $-\frac{10}{3}$
• D. $-3$

Answer 1

The correct option is B $-4$

Solve the equation:
$-2x+5y=1$.... (1)
$7x-10y=-11$.... (2)
Multiplying equation (1) with $2$:
$-4x+10y=2$
$+7x-10y=-11$
-----------------
$3x=-9$
$x=-3$
Substitute the value of $x$ in equation (1):
$-2(-3)+5y=1$

$6+5y=1$
$5y=-5$
$y=-1$
Sum of $x+y=-3-1=-4$