Answer
$$x = -5$$ $$y=2$$
Work Step by Step
Equation 1: $x - 3y = -11$
Equation 2: $4x + 5y = -10$
Using equation 1, add $3y$ to both sides:
$$x - 3y +3y= -11+3y$$ $$x = -11+3y$$
Substitute this equation to equation 2:
$$4x + 5y = -10$$ $$4(-11+3y) + 5y = -10$$ $$-44+12y + 5y = -10$$ $$-44+17y= -10$$
Add $44$ to both sides:
$$-44+44+17y= -10+44$$ $$17y=34$$ $$y=2$$
Substitute this value of $y$ to equation 1:
$$x - 3y = -11$$ $$x - 3(2) = -11$$ $$x - 6 = -11$$
Add $6$ to both sides:
$$x - 6+6 = -11+6$$ $$x = -5$$
Use equation 2 to check:
$$4x + 5y = -10$$ $$4(-5) + 5(2) = -10$$ $$-20 + 10 = -10$$ $$-10=-10$$