Question

How do you solve the system `x - y = 4` and `x + y = 2` by graphing?

Answer 1

Solution is `x=3` and `y=-1`

Explanation:

For solving the system `x-y=4` and `x+y=2` graphically, we should first draw these two lines.

`x-y=4` in slope of intercept form is `y=x-4` and hence it's intercept on `y` axis is `-4` and slope is `+1` i.e. positively sloping at `45^o`.

Similarly draw `x+y=2`, which in slope of intercept form is `y=-x+2` and hence it's intercept on `y` axis is `2` and slope is `-1` i.e. negatively sloping at `45^o`.

Please see the graph below. These two intersect at the point `(3,-1)`

Hence, solution is `x=3` and `y=-1`

graph{(x-y-4)(x+y-2)=0 [-10, 10, -5, 5]}