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

Jul 12, 2018

The solution is $\left(2 , - 1\right)$

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 $\left(1 , 0\right)$. Plot this point.

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

$0 + y = 1$

$y = 1$

The y-intercept is $\left(0 , 1\right)$. 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 $\left(3 , 0\right)$. Plot this point.

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

$0 - y = 3$

$- y = 3$

Divide both sides by $- 1$.

$y = \frac{3}{- 1}$

$y = - 3$

The y-intercept is $\left(0 , - 1\right)$. Plot this point.

Draw a line through the two points.

The point of intersection is the solution, which is $\left(2 , - 1\right)$.

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