# How do you solve linear quadratic systems?

**How to Solve using Algebra**

- Make both equations into "y =" format.
- Set them equal to each other.
- Simplify into "= 0" format (like a standard Quadratic Equation)
- Solve the Quadratic Equation!
- Use the linear equation to calculate matching "y" values, so we get (x,y) points as answers.

A.

### What is the difference between a linear and a quadratic equation?

A

**quadratic**equation is only**different**from a**linear**equation in one respect: one or more of the figures is squared. (The word**quadratic**derives from the Latin word for squared) The common form of a**quadratic**equation is ax^{2}+ bx + c = 11. In such a equation, if a = 1, b = 2 and c = 3 then X must equal 2.#### What are the methods for solving quadratic equations?

**There are several methods you can use to solve a quadratic equation:**- Factoring.
- Completing the Square.
- Quadratic Formula.
- Graphing.

#### What does a quadratic function look like in standard form?

f (x) = a(x - h)^{2}+ k, where (h, k)**is the**vertex of the parabola. FYI: Different textbooks have different interpretations of the reference "**standard form**" of a**quadratic function**. Some say f (x) = ax^{2}+ bx + c is "**standard form**", while others say that f (x) = a(x - h)^{2}+ k is "**standard form**".#### What is the zero factor principle?

The**Principle**of**Zero**Products states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0. Once the polynomial is factored, set each**factor**equal to**zero**and solve them separately. The answers will be the set of solutions for the original equation.

B.

### What is a linear quadratic system?

Solving a

**Linear**-**Quadratic System**. A**quadratic**equation is defined as an equation in which one or more of the terms is squared but raised to no higher power. The general form is ax^{2}+ bx + c = 0, where a, b and c are constants.#### What are linear quadratic and cubic polynomials?

A polynomial in the variable x is a function that can be written in the form, We have already seen degree 0, 1, and 2 polynomials which were the constant,**linear**, and**quadratic**functions, respectively. Degree 3, 4, and 5 polynomials also have special names:**cubic**, quartic, and quintic functions.#### What is the point of intersection called?

Two lines**intersect**when they cross each other. They form vertically opposite angles, which we will learn later. The**point**where the lines**intersect**is**called**the**point of intersection**. If the angles produced are all right angles, the lines are**called**perpendicular lines.#### How many planes can contain a line?

For example if the three points are A, B and C in your diagram then there are infinitely many planes that contain the points. I have illustrated**two**such planes in pink in the diagrams below. The final point is that if the three points do not lie on a line then there is exactly**one plane**that contains the points.

Updated: 2nd October 2019