## Algebra 1

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 $23=5(-5)-4(-12)$ $23=-25+48$ $23=23\checkmark$