Linear and Quadratic Equations

Linear equation

Equation with one or more variables in which each variable is raised only to the first power

Substitution method

Given two equations with two different variables, we can isolate one of the variables in either of the equations. Then you can insert the value into the other equation

Combination method

Given multiple equations, we can add or subtract one equation from another in order to eliminate one variable and solve for the other variable

Coefficient of the variable

Number that is multiplied by the variable

Manipulating the equations for combination by multiplying

When both equations do not have a matching coefficient of the variable

Solve for x in terms of y

Manipulate the equation such that x is isolated on one side of the equal sign (just x no variables) and the expression containing y is on the other

Common factor can be factored out

When all terms in the expression or equation have a common factor

Then either both integers are both 1 or -1

If the product of two integers is 1

Zero product property

If the product of two quantities is equal to 0, then at least one of the quantities has to be equal to 0

Quadratic equation

Equation in which the highest power of an unknown quantity is 2

Factors of quadratic expression

(X+p) and (x+q)

Roots/solutions of quadratic equation

The actually numbers for p and q that set it equal to 0 ex.

X=-1 or x=-8

FOIL

First, outside, inside, last

Discriminant

b² - 4ac part of the quadratic equation

Sum of two solutions = -b/a

Product of two solutions = c/a

Vieta’s formulas

(a-b)(a+b)

a² - b²