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Get Started Now- Intro Lesson2:34
- Lesson: 1a10:28
- Lesson: 1b3:19
- Lesson: 2a6:50
- Lesson: 2b6:53
- Lesson: 3a5:46
- Lesson: 3b3:20

The solutions to a system of equations are the points of intersection of their graphs. There are 3 cases you will come across when trying to solve the system. There can be 2 solutions, 1 solution or even no solutions.

Basic concepts: Solving systems of linear equations by graphing, Solving systems of linear equations by elimination, Solving systems of linear equations by substitution, Solving quadratic equations by factoring, Solving quadratic equations using the quadratic formula,

Related concepts: Graphing linear inequalities in two variables, Graphing systems of linear inequalities, Graphing quadratic inequalities in two variables, Graphing systems of quadratic inequalities,

- Introduction• 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

- 1.
**Case 1: System with 2 Solutions**a)Solve the system:

$y = - x + 1$

$y = {x^2} + x - 2$b)Verify the solutions graphically - 2.
**Case 2: System with 1 Solution**a)Solve the system:

$2x - y = 8$

$y = {x^2} - 4x + 1$b)Verify the solutions graphically - 3.
**Case 3: System with No Solutions**a)Solve the system:

$10x + 5y + 15 = 0$

$y = {x^2} - 4x + 2$b)Verify the solutions graphically

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