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.
sample response: both jared and nicole are correct. you can solve for either variable and use the equivalent expression to create a one - variable equation. then you can solve. jared would have created a one - variable equation that can be used to solve for ( x ), whereas nicole would have created a one - variable equation that can be used to solve for ( y ).
what did you include in your response? check all that apply
(square) both jared and nicole are correct
(square) you can solve for either variable and use the equivalent expression to create a one - variable equation
(square) jared would have created a one - variable equation that can be used to solve for ( x )
(square) nicole would have created a one - variable

Explanation:

Substitution method for systems of equations allows solving for either variable in one equation and substituting the equivalent expression into the other equation to form a single-variable equation. Jared solved for $y$ as $y=x+10$ and substituted, while Nicole rearranged the same equation to solve for $x$ as $x=y-10$ and substituted. Both approaches are valid applications of the substitution method, leading to a solvable single-variable equation (Jared's for $x$, Nicole's for $y$).

Answer:

• Both Jared and Nicole are correct.
• You can solve for either variable and use the equivalent expression to create a one-variable equation
• Jared would have created a one-variable equation that can be used to solve for $x$
• Nicole would have created a one-variable equation that can be used to solve for $y$