Question

Roxanne graphed this system of equations to find the solution.

Answer 1

Answer:

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

Step-by-step explanation:

The given equations are:

$y=\frac{2}{3}x-5$ 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

Answer:

Option C is correct.

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

Step-by-step explanation:

Given the system of equations:

$y = \frac{2}{3}x-5$         .....[1]

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

equate these two equations we get;

$\frac{2}{3}x-5=-2x+3$

Add 5 to both sides we get;

$\frac{2}{3}x = -2x+8$

Add 2x to both sides we have;

$\frac{8}{3}x = 8$

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.