Mini-test Project

Systems of Equations

What are the system of equations?

A system of equation is a pair of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.

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

Solving by Substitution

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?

Write a System

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.