Digits, Grade 8, Volume 1, Homework Helper

## Topic 8: Simultaneous Linear Equations

### 8-1: What are Simultaneous Linear Equations in Two Variables?

#### Key Concept

System of Linear Equations

One pencil and one marker cost \$1.50. Two pencils and one marker cost \$2.00. What are the cost of one pencil and the cost of one marker?

A system of simultaneous linear equations is two or more linear equations with the same two variables that are solved simultaneously. The solution of a system of simultaneous linear equations is any ordered pair (x, y) that is a solution of every equation in the system.

The solution of the system is (0.5, 1), the values for the variables p and m that make both equations true.

table with 3 rows and 4 columns , row1 column 1 , p plus m , column 2 equals 1.5 , column 3 2 p plus m , column 4 equals 2 , row2 column 1 , 0.5 plus 1 , column 2 modified modified question mark with under bar below with under bar below , 1.5 , column 3 2 open 0.5 close plus 1 , column 4 modified modified question mark with under bar below with under bar below , 2 , row3 column 1 , 1.5 , column 2 equals 1.5 u 2 , column 3 2 , column 4 equals 2 u 2 , end table

The solution of a system of simultaneous linear equations is the point of intersection of the graphs of the lines defined by the equations. End ofPage 263