Question

using substitution in different ways
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.

Explanation:

Both Jared and Nicole are using valid algebraic rearrangement and substitution, which are core methods for solving systems of equations. Jared rearranged the equation to isolate $y$, while Nicole rearranged the same original equation to isolate $x$; both forms are equivalent algebraic manipulations of the starting equation. Substituting either equivalent expression into the second equation will lead to the correct solution for the system.

Answer:

Both Jared and Nicole are correct. Jared isolated $y$ as $y = x + 10$ and substituted it, while Nicole rearranged the same equation to isolate $x$ as $x = y - 10$ and substituted it. Both are valid algebraic substitutions that will yield the correct solution to the system of equations.