Did I do this problem correctly?

Solve the following system by first handling the equation of the two lines:
x=(0, 2) y=(-2, 1)
x=(0, -1) y=(-3, -2)
Equation 1: y= -x1
Equation 2: y=4x/3+2T
Is this the correct answer?

No, neither is correct.

m= (y1-y2)/(x1-x2)

The slope of the first line is (using BobPursley's formula)

[1 -(-2)]/2 = 3/2

The y-intercept (where x=0) is -2.

Therefore the equation is y = 3x/2 - 2

Now you do the other line.

To check if your solution is correct, we need to substitute the given points into the equations and see if they hold true. Let's go through the process step by step.

Given:
Line 1:
x = (0, 2)
y = (-2, 1)
Equation 1: y = -x

Substituting the point (0, 2) into Equation 1:
2 = -(0)
2 = 0

This equation is not true, so Line 1 does not pass through the point (0, 2).

Line 2:
x = (0, -1)
y = (-3, -2)
Equation 2: y = 4x/3 + 2

Substituting the point (0, -1) into Equation 2:
-1 = 4(0)/3 + 2
-1 = 2

Again, this equation is also not true when substituting the point (0, -1).

Based on the results, it seems that your solution is not correct. You might have made an error while solving the system of equations or calculating the values. I recommend double-checking your work to ensure the accuracy of your solution.