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Graph the system of equations on your graph paper to answer the question. {y=x+2y=−x+8 What is the solution for this system of equations? Enter your answer in the boxes.

Respuesta :

calculista
using a graphical tool
 the solution is (3,5)  see the attached figure

y=x+2
y=-x+8
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ANSWER

[tex](3,5)[/tex]

EXPLANATION

The given systems of equations are;

[tex]y = x + 2[/tex]

and

[tex]y = - x + 8[/tex]

To graph the first function, which is

[tex]y = x + 2[/tex]

We need at least two points.

Let us use the intercepts.

At y-intercepts, x=0,

This implies that,

[tex]y = 0 + 2 = 2[/tex]

The y-intercept is,

[tex](0,2)[/tex]

At x-intercept, y=0.

This implies that,

[tex]0 = x + 2[/tex]
[tex]x = - 2[/tex]

The x-intercept is

[tex](-2,0)[/tex]

We plot the intercepts and draw a straight line through them to obtain the blue line on the graph in the attachment.

We repeat the same process for

[tex]y = - x + 8[/tex]

to obtain the y-intercept to be,

[tex](0,8)[/tex]

and the x-intercept to be,

[tex](8,0)[/tex]

We plot this one also on the the same graph to obtain the straight line in red.

The intersection of the two straight lines is

[tex](3,5)[/tex]

This the solution to the system of equations.
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