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 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.

Answer 2

They are both correct in their procedure. Nicole solved for one variable in the equation, while Jared solved for the other variable.

Explanation:

Notice that if you have the equation y = x + 10 in a system of equations, the most immediate thing to do is to try to use the fact that "y" is the same as "x + 10" to substitute in the other equation of the system.

But, this same equation can also be used to solve for the other variable "y", by simply subtracting 10 from both sides, which gives:

y - 10 = x

So now, one can use "y-10" to substitute for x in the other equation.

Both procedures are correct, and simply will lead to finding a different variable first when solving the equation.