Question

When solving a system of equations, Jared found y = x + 10 for one equation and substituted x + 10 for y in the other equation. Nicole found x = y – 10 for the same equation and substituted y – 10 for x in the other equation. Who is correct? Explain.

Answer 1

Both are correct. The two expressions are equivalent: from y = x + 10 you can subtract 10 from both sides to get x = y − 10. So you may substitute x + 10 for y in the other equation or substitute y − 10 for x — either substitution is algebraically the same and will lead to the same solution (or the same contradiction).

Example: if the other equation is x + y = 8,
- Substituting y = x + 10: x + (x + 10) = 8 → 2x + 10 = 8 → x = −1, y = 9.
- Substituting x = y − 10: (y − 10) + y = 8 → 2y − 10 = 8 → y = 9, x = −1.