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Try reviewing these fundamentals first.

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Try reviewing these fundamentals first.

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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

23.

Quadratic Equations

23.1

Characteristics of quadratic functions

23.2

Transformations of quadratic functions

23.3

Converting from general form to vertex form by completing the square

23.4

Solving quadratic equations by factoring

23.5

Solving quadratic equations by completing the square

23.6

Using quadratic formula to solve quadratic equations

23.7

Nature of roots of quadratic equations: the discriminant

23.8

System of linear equations

23.9

System of linear-quadratic equations

We have over 1180 practice questions in Algebra 1 for you to master.

Get Started Now23.1

Characteristics of quadratic functions

23.3

Converting from general form to vertex form by completing the square

23.4

Solving quadratic equations by factoring

23.5

Solving quadratic equations by completing the square

23.6

Using quadratic formula to solve quadratic equations

23.9

System of linear-quadratic equations