solving systems of equations

solve

3x=6y+2 x= 2y+3/2

Systems of equations

A set of two or more equations containing a set of common variables.

Graphing Linear Equations in Three Dimensions

Graph 6x + 3y - 4z = 12.

Systems of Linear Inequalities

Graph the system of inequalities. y ≥ 2x + 3 y > -x - 3

solving equations

In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equality sign.

a line set intersecting is what?

One solution

Sarah is selling bracelets and earrings to make money for summer vacation. The bracelets cost $2 and earrings cost $3. She needs to make at least $500. Write an inequality to represent the income from the jewelry sold. Sarah knows that she will see more than 50 bracelets. Write an inequality to represent this situation. Graph the two inequalities and shade the intersection. Identify a solution. How many bracelets and earrings can Sarah sell?

Sarah could sell 200 bracelets and 200 pairs of earrings.

y = mx+b

Slope-intercept form of a line; y = 3x - 5

solving systems with three variables

Solve the system of equations. 3x + 2y - z = 10 2x + y + z = -2 2x + 3y + z = 4

The Substitution Method

Solve this linear system of equations by the substitution method. x + 4y = 16 3x - 2y = 6

The Elimination Method

Solve this linear system using the elimination method. 3x - y = 3 x + y = 17

The Graphing Method

Solve this system of equations by graphing. y = 3x - 3 -4x + 2y = -6

Ax + By = C

Standard form of a line

Rate of Change

The ratio of vertical change to horizontal change

Slope

The steepness of a line

Zero Slope

a horizontal line

Negative Slope

falls from left to right

"the same line"?

infinitely many solutions

solve by elimination

multiply first by something to get rid of one variable then add equations together and sub answer into first equation

a parallel line set is what?

no solution

solve by substitution

put one equation into another to solve for the ordered pair

Positive slope

rises from left to right

inequality

the relation between two expressions that are not equal, employing a sign such as ≠ "not equal to," > "greater than," or < "less than.".

Undefined Slope

the slope of a vertical line

solve by graphing

use graph to solve