Question

Roxanne graphed this system of equations to find the solution.

Answer 1

(C) No, she use the wrong y intercepts when graphing the equations.

Explanation:

The given equations are:

`y=(2)/(3)x-5` and
`y=-2x+3`

Now, for graphing both the equations, we use hit and trial method by substituting the various values of x in the given equations,

When x=0,
`y=0-5=-5`, when x =3,
`y=2-5=-3`

When x=0,
`y=3`, when x=3,
`y=-6+3=-3`

Thus, the solution of both the equations is (3,-3).

Hence, option (C) No, she use the wrong y intercepts when graphing the equations is correct.

Answer 2

Option C is correct.

She is not correct as she use the wrong y intercepts when graphing the equations.

Explanation:

Given the system of equations:

`y = (2)/(3)x-5` .....[1]

`y = -2x+3` . .....[2]

equate these two equations we get;

`(2)/(3)x-5=-2x+3`

Add 5 to both sides we get;

`(2)/(3)x = -2x+8`

Add 2x to both sides we have;

`(8)/(3)x = 8`

Multiply both sides by 3 we get;

8x = 24

Divide both sides by 8 we get;

x = 3

Substitute the value of x in [2] we have;

y = -2(3)+3 = -6+3

Simplify:

y = -3

Therefore, the correct solution for this given system of equation is (3, -3)

You can see the graph of these equations below.