Question 114281
If you are asked to solve a system of linear equations by graphing, you just graph the two lines and the solution point is where the two lines intersect.  Like this:


{{{drawing(400, 400, -5,5,-5,5,grid(1),red(line(7,9,-8,-6)),green(line(10,-6,-2,6)))}}}


The red line is {{{y=x+2}}} and the green line is {{{y=-x+4}}} and we can see that they intersect at (1, 3).  That means that x = 1 and y = 3 will make both of the equations true.  Let's check that assertion:


{{{3 = 1 + 2}}} is true, and
{{{3 = -1 + 4}}} is also true.


The method of solving a system of two linear equations in two varibles by graphing works quite well as long as the solution is nice neat whole numbers and the intersection of the two lines is right on top of the intersection of two grid lines.  Other situations require other methods to get the exact answer, and you should be working on those other methods in your class the next few sessions.


Hope that helps.
John