Question

Solve the system of equations:
$-x-3y=-1$
$-2x+3y=-20$

Answer 1

Detailed step-by-step solution:
$-x-3y=-1$ ...eq(1)
$-2x+3y=-20$ ...eq(2)
Since the coefficient of $y$ in both the equations is the same but with the opposite sign, directly adding the equations will eliminate y from both the equations.
Adding equation (1) and equation (2), we get:
$-x-3y=-1$
$-2x+3y=-20$
$-3x+0=-21$
$\Rightarrow -3x=-21$
$x=\frac{-21}{-3}$ (dividing by $-3$ on both sides)
$\Rightarrow x=7$
Substituting the value of $x$ in equation (1), we get:
$-\left(7\right)-3y=-1$
$\Rightarrow -3y=-1+7$
$\Rightarrow -3y=6$
$x=\frac{6}{-3}$ (dividing by $-3$ on both sides)
$y=-2$

$\Rightarrow$ Option C is correct.