Answer
x=7
y=2
(7,2)
Work Step by Step
$3x-5y=11$
$2x-6y=2$
Equate the coefficients.
Multiply the first equation by 2.
$2(3x-5y)=2(11)\longrightarrow$ Simplify. Apply the distributive propety.
$6x-10y=22$
Multiply the second equation by 3.
$3(2x-6y)=3(2)\longrightarrow$ Simplify. Apply the distributive property.
$6x-18y=6$
Subtract the new equations.
$\ \ \ \ 6x-10y=22$
$\underline{-(6x-18y=6)}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8y=16$
Solve for y.
$8y=16\longrightarrow$ Divide both sides by 8.
$8y\div8=16\div8\longrightarrow$ Simplify.
$y=2$
Substitute for y in one equation and solve for x.
$3x-5(2)=11\longrightarrow$ Simplify.
$3x-10=11\longrightarrow$ Add 10 to both sides.
$3x-10+10=11+10\longrightarrow$ Simplify.
$3x=21\longrightarrow$ Divide both sides by 3.
$3x\div3=21\div3\longrightarrow$ Simplify.
$x=7$