Question

ernesto tried to determine the solution for the system of equations using substitution. his work is shown below.

\\(x - y = 7\\)
\\(3x - 2y = 8\\)

step 1: \\(x = y + 7\\)
step 2: \\(3(y + 7) - 2y = 8\\)
step 3: \\(3y + 7 - 2y = 8\\)
step 4: \\(y + 7 = 8\\)
step 5: \\(y = 1\\)

in which step did ernesto make the first error?

step 1
step 2
step 3
step 4

Explanation:

Analyze the system and Step 1

The given system of equations is:

$$
LATEXBLOCK0
$$

In Step 1, Ernesto solves the first equation for \(x\):

$$ x = y + 7 $$

This step is correct.

Analyze Step 2

In Step 2, Ernesto substitutes \(x = y + 7\) into the second equation:

$$ 3(y + 7) - 2y = 8 $$

This substitution is correct.

Analyze Step 3

In Step 3, Ernesto simplifies the equation from Step 2:

$$ 3(y + 7) - 2y = 8 \implies 3y + 21 - 2y = 8 $$

However, Ernesto wrote:

$$ 3y + 7 - 2y = 8 $$

He failed to distribute the \(3\) to the \(7\) inside the parentheses. Thus, Step 3 contains the first error.

Answer:

• Step 1
• Step 2
• Step 3 (Correct answer)
• Step 4