[tex]\sf{y=x-5}[/tex]
[tex]\sf{3x+y=7}[/tex]
Lets solve this by substitution.
Lets plug in y=x-5 into 3x+y=7
So:
[tex]\sf{y=x-5}[/tex]
[tex]\sf{3x+y=7}[/tex]
Plugging it in:
[tex]\sf{3x+(x-5)=7}[/tex]
Solve for x by simplifying that:
[tex]\sf{3x+x-5=7}[/tex]
[tex]\sf{4x-5=7}[/tex]
Add 5 on both sides
[tex]\sf{4x=12}[/tex]
Divide by 4 on both sides
[tex]\sf{x=3}[/tex]
Now simply plug x=3 back into any equation and solve for y
So:
[tex]\sf{y=x-5}[/tex]
[tex]\sf{y=3-5}[/tex]
Simplify that:
[tex]\sf{y=-2}[/tex]
So we are left with our final answer which is
[tex]\boxed{\bf{(3,-2)}}[/tex]
