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+21 - 2y = 8
step 4: y + 21 = 8
step 5: y = - 13

in which step did ernesto make the first error?
o step 1
o step 2
o step 3
o step 4

Explanation:

Step1: Analyze substitution method

The substitution method for a system of equations \(x - y=7\) (so \(x=y + 7\)) and \(3x-2y = 8\) should start by substituting \(x=y + 7\) into \(3x-2y=8\). In Step 1, the substitution is done correctly as \(3(y + 7)-2y=8\).

Step2: Expand the expression

Expanding \(3(y + 7)-2y=8\) gives \(3y+21 - 2y=8\), not \(3y + 7-2y=8\) as in Step 2. The error is in the expansion of \(3(y + 7)\) where the distributive property was not applied correctly. \(3(y + 7)=3y+21\), not \(3y + 7\).

Answer:

Step 2