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

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

y=x+2
y=-x+8

Answer 2

ANSWER


`(3,5)`

Step-by-step 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.