Question

Consider the system of equation:
y = -2x + 4
y = -1/3x - 1
The solution is (3, -2). When verifying the solution, what does your final step look like?

A. 4 = 4
B. -3 = -3
C. -1 = -1
D. -2 = -2

Answer 1

To verify the solution (3, -2) for the system of equations:

1. Substitute \( x = 3 \) and \( y = -2 \) into the first equation:
\[
y = -2x + 4
\]
\[
-2 = -2(3) + 4
\]
\[
-2 = -6 + 4
\]
\[
-2 = -2 \quad (\text{This statement is true.})
\]

2. Now substitute \( x = 3 \) and \( y = -2 \) into the second equation:
\[
y = -\frac{1}{3}x - 1
\]
\[
-2 = -\frac{1}{3}(3) - 1
\]
\[
-2 = -1 - 1
\]
\[
-2 = -2 \quad (\text{This statement is also true.})
\]

In both cases, the final statements we arrive at are true. However, you need to determine which option corresponds to the verification.

For the first equation, we ended with:
\[
-2 = -2
\]

Thus, the final step that aligns with our solution verification is:
**D. -2 = -2**.