# How do you solve the system -x + y=3 and x+ y=5 by graphing?

Dec 7, 2015

Draw the lines for the given equations and take the point of intersection as the solution.
Note that the accuracy of your solution will depend upon the accuracy of your graphing.

#### Explanation:

Using the intercepts:
for $- x + y = 3 \rightarrow \left(- 3 , 0\right) , \left(0 , 3\right)$
for $x + y = 5 \rightarrow \left(5 , 0\right) , \left(0 , 5\right)$
We can plot the lines for these tow equations:
graph{(-x+y-3)(x+y-5)((x+3)^2+y^2-0.01)(x^2+(y-3)^2-0.01)((x-5)^2+y^2-0.01)(x^2+(y-5)^2-0.01)=0 [-4.707, 6.394, -0.35, 5.197]}
Examining the graph we see that the point of intersection is (at least approximately) $\left(1 , 4\right)$