Question

Solve the system by graphing. Write the solution as an ordered pair. y = 1/3x + 2 y = –x – 2

Help me please....I need good grades

Answer 1

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jh24

Explanation:

Answer 2

ANSWER

The solution is where the two graphs intersect, which is

`(-3,1).`

EXPLANATION

The given system of equations are

`y = (1)/(3) x + 2`
and


`y = - x - 2`

We need to graph the two equations.

Let us graph


`y = (1)/(3) x + 2`
first.

We need at least two points.

You can choose any appropriate value for x and solve for y. Choosing zero makes our working easier. So let us plot the intercepts.

When

`x = 0`


`\Rightarrow \: y = (1)/(3) (0) + 2`


`\Rightarrow y = 0 + 2`


`\Rightarrow y = 2`

So this gives us the ordered pair,


`(0,2)`

When

`y = 0`
we get,


`0= (1)/(3) x + 2`


`\Rightarrow \: - 2 = (1)/(3) x`


`\Rightarrow \: - 2 * 3= x`


`\Rightarrow \: -6= x`
This also gives the ordered pair


`(-6,0).`

We plot these two points and draw a straight line through them to obtain the blue graph in the attachment.

For the second line


`image`

We again find the intercepts and plot them.

When

`x = 0`


`y = - 0 - 2`


`\Rightarrow \: y = - 2`

This gives the ordered pair


`(0,-2)`

Also, when

`y = 0`

then we have,


`0 = - x - 2`


`2 = - x`


`x = - 2`

Then we again have the ordered pair,


`(-2,0)`

We plot these two points on the same graph sheet to obtain the red graph above.

The intersection of the two lines is

`(-3,1)`


You will get good grades so don't worry much.