# System of Equations

### By: Carter Colclasure

## A System of Equations

A system of equations is a group of linear equations involving the same set of variables. There are three ways to solve the equations. You can graph, use substitution, or use elimination. You solve for the variables and the multiple variables will be your answer

## Graphing

If the two linear equations in the system are in slope-intercept form then you should solve it by graphing. The interception points of the two lines are two variables

2x+7y=14 First I changed both equations into slope intercept form then I graphed

5x+7y=-7 them. The interception point was (-7,4) .

## Substitution

When using substitution you substitute one of the variables with an equation to fin out how to do this watch the

## Elimination

It is good to use elimination when the system of equations are both in standard form. You make the both x or y values the same number but one negative. Then you simply add the equations together and solve

## Writing a System

In a word problem you first read it then you identify the two equations, here is a word problem.

You pay $24.50 for 10 gallons of gasoline and 1 quart of oil at the gas station. Your friend pays $22 for 8 gallons of the same gasoline and and 2 quarts of oil. Find the cost of 1 quart of oil.

## Word Problem

A rental car 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 four hours and pays $63. Another rents a floor sander for 6 hours and pays $87. Find the flat fee and the cost per hour.