# Mini-test Project

### Systems of Equations

## What are the system of equations?

A system of linear equations can be solved three different ways. They are

Substitution, Elimination, and Graphing. It can be presented by Write a System or Word problems. Than the solution will represent either Infinitely many, One solution, and No solution.

## Graphing - 500

**Problem**

**2x + 7y = 14**

**5x + 7y = 7**

## Substitution - 200

**Problem**

**x = y - 11**

**x - 3y = 1**

## Substitution - 400

**Problem**

**4.5x + 1.5y = 24**

**x - y = 4**

## Elimination - 500

**Problem**

**3y = x + 5**

**3x + 8y = 8**

## Write a System - 400

**Problem**

**The width of a rectangular plot of land is 16 yards less **

**than the length. The perimeter of the land is 208 yards. **

**What is the length and width of the land?**

## Word Problems - 500

**Problem**

**A rental company charges a flat fee of x dollars **

**for a floor sander rental plus y dollars per hour of **

**the rental. One customer rents a floor sander for **

**4 hours and pays $63. Another customer rents a **

**floor sander for 6 hours and pays $87. Find the**

**flat fee and the cost per hour for the rental.**

## When it's best to use Substitution

It is best used when on variable of an equation is isolated, most likely in slope intercept form.

Example:

2x+y=5

y=x-4

## When it's best to use Elimination

It is best used when two equations are in standard form or the variables line up. Also if one of the same variables in negative and the other is positive but have the same variable, so they can cancel out.

Example:

3x + 3y =15

2x - 3y = 5

## When it's best to use Graphing

It is best used when the two equations are in slop-intercept form.

Example:

y=x+3

y=2x+4

## 3 Types of Solutions

**One solution**is when there is one answer to the problem or one point.

**No solution**is when there is no solution to the problem.

**Infinitely many solution**is when there is a infinite amount of answers, the answers equal each other.

## One Solution If you find two lines are crossing at one point the system of equations has one solution. | ## No SolutionIf you find the two lines are parallel and do not cross at any point the system has no solutions. | ## Infinity SolutionIf you find the two lines lie on top of one another the system has an infinite number of solutions. |

## One Solution

## No Solution

If you find the two lines are parallel and do not cross at any point the system has no solutions.