Question

Using a sheet of graph paper, solve the following system of equations graphically. Be sure to show any work, use a straight edge, and be neat. When you are finished, enter the solution set in the box below and turn in your graph paper to your teacher.
x + y = 0
x - y + 2 = 0

Answer 1

we have the following system of equations

$x + y = 0\\x - y + 2 = 0$

we know that

The intersection of both graphs is the solution of the system of equations

using a graph tool

see the attached figure

the solution is the point $(-1,1)$

therefore

the answer is

the solution of the system of equations is the point $(-1,1)$

Answer 2

Answer:

The solution of given system of equations is (-1,1).

Step-by-step explanation:

The given equation are

$x+y=0$               ..... (1)

$x-y+2=0$            ..... (2)

Add both equations.

$x+y+x-y+2=0$

$2x+2=0$

Subtract both sides by 2.

$2x+2-2=0-2$

$2x=-2$

Divide both sides by 2.

$x=-1$

Put this value in equation 1.

$-1+y=0$

Add 1 on the both sides.

$-1+y+1=0+1$

$y=1$

Therefore the solution of given system of equations is (-1,1).

Solution of system of equation graphically.

Plot both lines on the graph.

Put x=0, the find the y-intercept of both equations.

$(0)+y=0\Rightarrow y=0$

Put x=1, the find the y-intercept of both equations.

$(1)+y=0\Rightarrow y=-1$

Therefore first line passing through the points (0,0) and (1,-1).

Put x=0, the find the y-intercept of both equations.

$(0)-y+2=0\Rightarrow y=2$

Similarly, put y=0 in second equation.

$x-(0)+2=0\Rightarrow x=-2$

y-intercept of second equation is (-2,0).

Therefore second line passing through the points (0,2) and (-2,0).

From the graph it is noticed that both the line intersect on the point (-1,1), therefore  solution of given system of equations is (-1,1).