System of linear-quadratic equations

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Intros

Lessons

• The solutions to a system of equations are the points of intersection of the graphs.
• For a system consisting of a linear equation and a quadratic equation:
linear equation: $y = mx + b$
quadratic equation: $y = a{x^2} + bx + c$
There are 3 cases to consider:

case 1: 2 solutions case 2: 1 solution case 3: no solutions

Examples

Lessons

Case 1: System with 2 Solutions
1. Solve the system:
  $y = - x + 1$
  $y = {x^2} + x - 2$
2. Verify the solutions graphically
Case 2: System with 1 Solution
1. Solve the system:
  $2x - y = 8$
  $y = {x^2} - 4x + 1$
2. Verify the solutions graphically
Case 3: System with No Solutions
1. Solve the system:
  $10x + 5y + 15 = 0$
  $y = {x^2} - 4x + 2$
2. Verify the solutions graphically

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