Question 137848
1.{{{x-y=5}}}
2.{{{x+2y=7}}}
There are many ways to solve this system of linear equations.
I'll use the substitution method. 
Use equation 1, to solve for x in terms of y.
1.{{{x-y=5}}}
{{{x=y+5}}}
Now use this value and substitute for x in equation 2.
2.{{{x+2y=7}}}
{{{(y+5)+2y=7}}}
{{{3y+5=7}}}
Now solve for y.
{{{3y=2}}}
{{{y=2/3}}}
You can work backwards and find x now that you have y.
{{{x=y+5}}}
{{{x=(2/3)+5}}}
{{{x=(2/3)+(15/3)}}}
{{{x=17/3}}}
Always check your answers.
Use your original equations.
1.{{{x-y=5}}}
{{{(17/3)-(2/3)=5}}}
{{{15/3=5}}}
{{{5=5}}}
True statement.
Good answer.
2.{{{x+2y=7}}}
{{{(17/3)+2(2/3)=7}}}
{{{(17/3)+(4/3)=7}}}
{{{21/3=7}}}
{{{7=7}}}
True statement.
Good answer.
{{{x=17/3}}}
{{{y=2/3}}}