Question

Danny attempted to solve the following system of equations using SUBSTITUTION but made a mistake. Find the error.

x−y=7
2x+y=8

Answer 1

To solve the system of equations using substitution, express one variable in terms of the other and substitute it into the second equation. Then solve for the remaining variable.

Step-by-step explanation:

Danny attempted to solve the system of equations using substitution, but made a mistake. Let's go through the correct steps to solve the system:

1. From the first equation, we can express x in terms of y as x = 7 + y.
2. Substitute this value of x into the second equation:
3. 2(7 + y) + y = 8
4. Now simplify the equation: 14 + 2y + y = 8
5. Combine like terms: 3y + 14 = 8
6. Subtract 14 from both sides: 3y = -6
7. Divide both sides by 3: y = -2
8. Substitute this value of y back into the expression for x: x = 7 - 2 = 5

Therefore, the correct solution to the system of equations is x = 5 and y = -2.