Berta worked to solve a system of equations.

Question

4x + y = –5

x – y = –5

Step 1: ???

Step 2: x = –2

Step 3: 4(–2) + y = –5

Step 4: –8 + y = –5

Step 5: y = 3

Berta determined that the solution is (–2, 3).

Which could have been the equation Berta found in step 1?
4x = 0
5x = 10
5x = –10
5x = –25

Answer 1

To find the equation Berta might have written in Step 1, we need to consider how she got to Step 2, where she found that \( x = -2 \).

The equation she used in Step 3, \( 4(-2) + y = -5 \), suggests that she substituted \( x = -2 \) back into one of the original equations to solve for \( y \).

Since she was clearly solving the system of equations composed of:

1. \( 4x + y = -5 \)
2. \( x - y = -5 \)

We need to focus on a potential equation for Step 1 that logically leads to finding \( x = -2 \).

We can express \( y \) in terms of \( x \) using the second equation:

• From \( x - y = -5 \), we can rearrange it to \( y = x + 5 \).

Substituting this expression for \( y \) back into the first equation: \[ 4x + (x + 5) = -5 \] Combine similar terms: \[ 4x + x + 5 = -5 \ 5x + 5 = -5 \ 5x = -10 \] This simplification gives us \( 5x = -10 \), indicating this could have been an equation Berta could have written in Step 1.

Now evaluating the options provided:

1. \( 4x = 0 \)
2. \( 5x = 10 \)
3. \( 5x = -10 \) <-- This is the equation we derived.
4. \( 5x = -25 \)

Thus, the equation Berta might have found in Step 1 is:

5x = -10.