Question

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.

Answer 1

ANSWER

$(3,5)$

EXPLANATION

The given systems of equations are;

$y = x + 2$

and

$y = - x + 8$

To graph the first function, which is

$y = x + 2$

We need at least two points.

Let us use the intercepts.

At y-intercepts, x=0,

This implies that,

$y = 0 + 2 = 2$

The y-intercept is,

$(0,2)$

At x-intercept, y=0.

This implies that,

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

The x-intercept is

$(-2,0)$

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

$y = - x + 8$

to obtain the y-intercept to be,

$(0,8)$

and the x-intercept to be,

$(8,0)$

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

$(3,5)$

This the solution to the system of equations.

Answer 2

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

y=x+2
y=-x+8