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 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 = 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 In which step did Ernesto make the first error? Step 1 Step 2 Step 3 Step 4

Ernesto made his first error in Step 3 because he failed to apply the distribution property properly. It should be 3y + 21 - 2y = 8 instead of 3y + 7 – 2y = 8.

Solution to the System of Equations

Using the substitution method, the solution to a system of equations is solved by finding one variable in one of the equations, then substituting it to find the other variable.

Given, the systems of equations as:

x – y = 7 -- > eqn. 1
3x – 2y = 8 --> eqn. 2

Thus, Ernesto made his first error in Step 3 because he failed to apply the distribution property properly. It should be 3y + 21 - 2y = 8 instead of 3y + 7 – 2y = 8.

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