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

1 Answer
Jul 12, 2018

Answer:

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]}