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 principle

The substitution method involves solving one - equation for one variable and substituting it into the other equation. In Step 1, if we have the system of equations \(x - y=7\) and \(3x - 2y = 8\), solving \(x - y=7\) for \(x\) gives \(x=y + 7\). Then we substitute \(x=y + 7\) into \(3x-2y = 8\). But in the given Step 1 work shown as \(x=y + 7\) and then substituting into \(3x-2y = 8\) should result in \(3(y + 7)-2y = 8\), not the incorrect substitution shown in the problem (assuming the work has an error). The error is likely in the substitution process in Step 1.

Answer:

Step 1