Question

How do you draw the solution for `x+y= -1` and `x-y=3`?

Answer 1

The solution is `(2,-1)`

Explanation:

Equation 1: `x+y=1`

Equation 2: `x-y=3`

Drawing the solution means graphing the solution. For linear equations in standard form, it is easy to find the x- and y-intercepts, which can be plotted for each line, and a straight line can be drawn through the two points. You should plot each line separately and then determine the solution, which is the point of intersection of the two lines.

X-intercept: value of `x` when `y=0`

Y-intercept: value of `y` when `x=0`

Equation 1

x-intercept: substitute `0` for `y` and solve for `x`.

`x+0=1`

`x=1`

The x-intercept is `(1,0)`. Plot this point.

y-intercept: substitute `0` for `x` and solve for `y`.

`0+y=1`

`y=1`

The y-intercept is `(0,1)`. Plot this point.

Draw a straight line through the two points.

Equation 2

`x-y=3`

x-intercept: substitute `0` for `y` and solve for `x`.

`x-0=3`

`x=3`

The x-intercept is `(3,0)`. Plot this point.

y-intercept: substitute `0` for `x` and solve for `y`.

`0-y=3`

`-y=3`

Divide both sides by `-1`.

`y=3/(-1)`

`y=-3`

The y-intercept is `(0,-1)`. Plot this point.

Draw a line through the two points.

The point of intersection is the solution, which is `(2,-1)`.

graph{(x+y-1)(x-y-3)=0 [-10, 10, -5, 5]}