Question

Examine Kaitlyn’s steps for solving the system of equations.

–3x + 2y = 8
 3x + 2y = –6

Step 1: 4y = 2

Step 2: y = 2

Step 3: –3x + 2(2) = 8

Step 4: –3x = 4

Step 5: x = –1.333

Kaitlyn found the solution to be (1.3, 2). Is her solution correct? Explain.

Yes, she correctly solved the system of equations.
No, she made an error in step 1. The y variable should have been eliminated when adding the system of equations.
No, she made an error in step 2. She should have found y = 0.5.
No, she substituted y into the wrong equation to solve for x in step 3.

Answer 1

To evaluate Kaitlyn's solution to the system of equations:

1. **Start with the original equations**:
\[
-3x + 2y = 8 \quad \text{(1)}
\]
\[
3x + 2y = -6 \quad \text{(2)}
\]

2. **Add the two equations to eliminate \(y\)**:
\[
(-3x + 2y) + (3x + 2y) = 8 + (-6)
\]
This simplifies to:
\[
4y = 2
\]
which is correct as Kaitlyn states in Step 1.

3. **Solve for \(y\)**:
\[
y = \frac{2}{4} = 0.5
\]
However, Kaitlyn stated \(y = 2\) in Step 2. This is an error.

4. **Now substitute \(y\) back into one of the original equations to find \(x\)**:
We can substitute into equation (1):
\[
-3x + 2(0.5) = 8
\]
Simplifying gives:
\[
-3x + 1 = 8
\]
\[
-3x = 8 - 1
\]
\[
-3x = 7
\]
\[
x = -\frac{7}{3} \approx -2.33
\]

From this examination, here are the conclusions:

- No, she made an error in step 2. She should have found \(y = 0.5\).
- Also, since her \(y\) substitution is incorrect, her calculation for \(x\) is consequently also incorrect.

Thus, the correct answer to whether Kaitlyn's solution is correct is:
**No, she made an error in step 2. She should have found y = 0.5.**