System of Equations Using the Substitution Method with Nonlinear Equations

Solve System of Equations Substitution Method - Part 2 - How it Works - Video

Which Variable to Solve For

Which Variable to Solve For:

We have 4 options when dealing with 2 equations in a system of equations. We can solve for x or y for the nonlinear equation or we can solve for x or y for the linear equation. Each one has their own pros and cons, and that depends on you.

We are going to use x = 2y + 3.

Example 1 - Substitute

Example 1 Substitute:

Here we have solved for the variable x in x - 2y = 3 and our result is x = 2y + 3. We have to substitute this equation into our other equation, x + y² = 6.

Example 1 - Solve for the 1st Variable

Example 1 Solve for the 1st Variable:

Here we have solved for the variable x in x - 2y = 3 and our result is x = 2y + 3. We have to substitute this equation into our other equation, x + y² = 6.

We have factored and now we have two equations y + 3 = 0 and y - 1 = 0 so y = -3 and y = 1.

Example 1 - Plot 1st Equation

Example 1 Plot 1st Equation:

We have factored and now we have two equations y + 3 = 0 and y - 1 = 0 so y = -3 and y = 1.

Now that we know y = -3 and y =1. We can substitute in either question to find the x part of the ordered pair. Here we chose the linear equation.

So our points are (-3, -3) and (5, 1).

Example 1 - Plot 2nd Equation

Example 1 Plot 2nd Equation:

We know the points (-3, -3) and (5, 1) are also true for our 2nd equation. We know that is a parabola, which means we need our vertex. To find our vertex since we have a sideways parabola, we can use the formula y = -b / (2a). Which one is a? Which one is b? We look at the standard form, x = ay² + by + c. We have x = -1y² + 0y + 6, so a = -1, b = 0, and c = 6.

So x is 6, which means our point is (6, 0). Now we can graph our sideways parabola, and our solutions are the points (-3, -3) and (5, 1)

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