# How do you solve the system by graphing given x + y = 4 and –x + y = 2? Thanks in advance for any help at all on this one!?

Mar 27, 2015

You can give values of $x$ and evaluate the corresponding $y$ for the two equations.
By plotting the points obtained you'll be able to "see" the point where your lines cross each other:
Have a look:

Mar 27, 2015

the software here won't let us put two lines on the same garaph, so I'll post them separately and you'll have to put them on one coordinate system:

$x + y = 4$ is a linear equation. Its graph is a line.
You could get two points and connect the dots.
Or you could solve for $y$ to get slope-intercept form:
$x + y = 4$ subtract $x$ (add $- x$ on both sides to get:
$y = - x + 4$

Graph: graph{y=-x+4 [-6.54, 13.46, -2.64, 7.36]}

Now graph $- x + y = 2$ which is the same as $y = x + 2$

graph{y=x+2 [-6.54, 13.46, -2.64, 7.36]}

Look at the graph to see where the lines intersect.

.

Both lines contain the point $\left(1 , 3\right)$.

$x = 1$, and $y = 3$ makes both equations true, so it is a solution to the system.