Answer
$$x=3$$ $$y=2$$
Work Step by Step
Equation 1: $x + 4y = 11$
Equation 2: $5x - 9y = -3$
Solve the system using substitution method.
Using equation 1, subtract $4y$ from both sides:
$$x + 4y -4y= 11-4y$$ $$x = 11-4y$$
Substitute this equation to equation 2:
$$5(11-4y)- 9y = -3$$ $$55-20y- 9y = -3$$ $$55-29y=-3$$
Subtract $55$ from both sides:
$$55-55-29y=-3-55$$ $$-29y=-58$$
Divide both sides by $-29$
$$\frac{-29y}{-29}=\frac{-58}{-29}$$ $$y=2$$
Substitute this value of $y$ to equation 1:
$$x+4(2)=11$$ $$x+8=11$$
Subtract $8$ from both sides:
$$x+8-8=11-8$$ $$x=3$$
Use equation 2 to check:
$$5(3)-9(2)=-3$$ $$15-18=-3$$ $$-3=-3$$
