Answer
(-12,-5)
Work Step by Step
Solve for x in the first equation.
$2=2y-x\longrightarrow$ subtract 2 and add x to each side
$2-2+x=2y-x-2+x\longrightarrow$ combine like terms
$x=2y-2$
Substitute for x in the second equation and solve for y.
$23=5y-4x\longrightarrow$ substitute for y
$23=5y-4(2y-2)\longrightarrow$ multiply using the distributive property
$23=5y-8y+8\longrightarrow$ combine like terms
$23=-3y+8\longrightarrow$ subtract 8 from each side
$23-8=-3y+8-8\longrightarrow$ combine like terms
$15=-3y\longrightarrow$ multiply each side by -3
$15\div-3=-3y\div-3\longrightarrow$ multiply
$-5=y$
Substitute for y in the first equation to find x.
$2=2y-x\longrightarrow$ substitute for y
$2=2(-5)-x\longrightarrow$ multiply
$2=-10-x\longrightarrow$ add 10 to each side
$2+10=-10-x+10\longrightarrow$ add
$12=-x\longrightarrow$ multiply each side by -1
$12\times-1=-x\times-1\longrightarrow$ multiply
$-12=x$
Check the answer by substituting for x and y in each equation.
$2=2y-x\longrightarrow$ substitute
$2=2(-5)-(-12)\longrightarrow$ multiply
$2=-10+12\longrightarrow$ add
$2=2\checkmark$
$23=5y-4x\longrightarrow$ substitute
$23=5(-5)-4(-12)$
$23=-25+48$
$23=23\checkmark$
