Answer
x=-5
y=3
(-5,3)
Work Step by Step
$\frac{x}{3}+y=\frac{4}{3}$
$-x+2y=11$
Use substitution to solve.
Isolate one variable in one equation.
$\frac{x}{3}+y=\frac{4}{3}\longrightarrow$ Subtract $\frac{x}{3}$ from both sides.
$\frac{x}{3}+y-\frac{x}{3}=\frac{4}{3}-\frac{x}{3}\longrightarrow$ Simplify
$y=\frac{4}{3}-\frac{x}{3}$
Substitute for y in the other equation and solve for x.
$-x+2(\frac{4}{3}-\frac{x}{3})=11\longrightarrow$ Apply the distributive property.
$-x+\frac{8}{3}-\frac{2x}{3}=11\longrightarrow$ Multiply both sides by 3.
$3(-x+\frac{8}{3}-\frac{2x}{3})=3(11)\longrightarrow$ Apply the distributive property.
$-3x+8-2x=33\longrightarrow$ Combine like terms.
$-5x+8=33\longrightarrow$ Subtract 8 from both sides.
$-5x+8-8=33-8\longrightarrow$ Simplify.
$-5x=25\longrightarrow$ Divide both sides by -5.
$-5x\div-5=25\div-5\longrightarrow$ Simplify.
$x=-5$
Substitute for x in one equation and solve for y.
$-(-5)+2y=11\longrightarrow$ Simplify.
$5+2y=11\longrightarrow$ Subtract 5 from both sides.
$5+2y-5=11-5\longrightarrow$ Simplify.
$2y=6\longrightarrow$ Divide both sides by 2.
$2y\div2=6\div2\longrightarrow$ Simplify.
$y=3$
