Question

Solve $3x-5y=-16,2x+5y=31$

Answer 1

The given equations are
$3x-5y=-16$ (1)
$2x+5y=31$ (2)
Note that the coefficients of y in both equations are numerically equal. So, we can eliminate y easily.
Adding (1) and (2), we obtain an equation
$5x=15$
That is, $x=3$ (3)
Now, we substitute x = 3 in (1) or (2) to solve for y.
Substituting x = 3 in (1) we obtain, $3\left(3\right)-5y=-16$
$\to y=5$
Now, (3, 5) a is solution to the given system because (1) and (2) are true when x = 3 and y = 5 as from (1) and (2) we get, $3\left(3\right)-5\left(5\right)=-16$ and $2\left(3\right)+5\left(5\right)=31$.