Question

Create a system of equations that includes one linear equation and one quadratic equation.Part 1. Show all work in solving your system of equations algebraically.

Part 2. Graph your system of equations and show the solution graphically to verify your solution.

Answer 1

The simplest system:

y = x

y = x²

Solve by eliminating y:

x² = x

x(x - 1) = 0

x₁ = 0

x₂ = 1

Then the value of y:

y₁ = 0

y₂ = 1

The graphical solution is attached

(0, 0), (1, 1)

Explanation:

Answer 2

The simplest system:

• y = x
• y = x²

Solve by eliminating y:

• x² = x
• x(x - 1) = 0
• x₁ = 0
• x₂ = 1

Then the value of y:

• y₁ = 0
• y₂ = 1

The graphical solution is attached

• (0, 0), (1, 1)