Answer
x=1
y=-2
(1,-2)
Work Step by Step
$5x+2y=1$
$x-3y=7$
Equate the coefficients by multiplying the second equation by 5.
$x-3y=7\longrightarrow$ Multiply both sides of the equation by 5.
$5(x-3y)=5(7)\longrightarrow$ Simplify. Apply the distributive property.
$5x-15y=35$
Subtract the new equation from the first equation to eliminate x and solve for y.
$\ \ \ \ \ 5x+2y=1$
$\underline{-(5x-15y=35)}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ 17y=-34$
$17y=-34\longrightarrow$ Divide both sides by 17.
$17y\div17=-34\div17\longrightarrow$ Simplify.
$y=-2$
Substitute for y and solve for x.
$x-3(-2)=7\longrightarrow$ Simplify.
$x-(-6)=7$
$x+6=7\longrightarrow$ Subtract 6 from both sides.
$x+6-6=7-6\longrightarrow$ Simplify.
$x=1$
