# What is the final step of completing a solve by substitution problem?

##### 1 Answer

I'm not sure where exactly you mean "final" in the solving process. So, I've prepared a couple of problems that I will work through slowly and carefully, showing all the steps to the final answer.

**Example 1: Solve the following system of equations- #2x + y = 5, 3x + 2y = 9#**

Since we want to solve with substitution, we must solve for one variable in one of the equations. I think it would be easiest to solve for

We can now substitute into the other equation:

We must now find the value of

Hence, our solution set is

**Example 2: Find all real values of #x# and #y# that satisfy the following system of equations: #3y = -2x^2 + 2, 2x^2 - 3y^2 = -4#**

Once again, as with the last example, we need to solve for one of the variables in one of the equations. It looks easiest to isolate the

We can now substitute into equation #2.

Solve using a graphing calculator. If it's a standard one, like a TI84, use

This will give you real roots of

Hence, our solution set is

Use the following practice exercises to develop your comfort with the skills dealt with in this answer.

**Practice exercises:**

- Find the real values of
#x# and#y# that satisfy the following systems of equations.

a)

b)

c)

Hopefully this helps, and good luck!