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

ernesto tried to determine the solution for the system of equations using substitution. his work is shown below.\n$x - y = 7$\n$3x - 2y = 8$\nstep 1: $x = y + 7$\nstep 2: $3(y + 7)-2y = 8$\nstep 3: $3y + 7-2y = 8$\nstep 4: $y + 7 = 8$\nstep 5: $y = 1$\nin which step did ernesto make the first error?\n○ step 1\n○ step 2\n○ step 3\n○ step 4

ernesto tried to determine the solution for the system of equations using substitution. his work is shown below.\n$x - y = 7$\n$3x - 2y = 8$\nstep 1: $x = y + 7$\nstep 2: $3(y + 7)-2y = 8$\nstep 3: $3y + 7-2y = 8$\nstep 4: $y + 7 = 8$\nstep 5: $y = 1$\nin which step did ernesto make the first error?\n○ step 1\n○ step 2\n○ step 3\n○ step 4

Answer

Answer:

Step 3

Explanation:

Step1: Analyze Step 1

Isolate x from $x - y=7$, get $x=y + 7$. Correct.

Step2: Analyze Step 2

Substitute $x=y + 7$ into $3x-2y = 8$, get $3(y + 7)-2y=8$. Correct.

Step3: Analyze Step 3

Expand $3(y + 7)-2y=8$. Using distributive property $a(b + c)=ab+ac$, we should have $3y+21 - 2y=8$, not $3y + 7-2y=8$. Error here.