Chapter 7.1 Notes: Solve Linear Systems by Graphing Goal: You will solve a system of linear equations graphically.

A system of linear equations, or simply a linear system, consists of two or more linear equations in the same variable. A solution of a system of linear equations in two variables is an ordered pair that is a solution of each equation in the system.

There are three methods to solve linear systems, which are: – Graphing – Substitution – Elimination

Solving a Linear System Using the Graph-and- Check Method: Step 1: Make sure both equations in the linear system are written in slope-intercept form (y=mx+b). Step 2: Graph both equations in the same coordinate plane. Step 3: Estimate the coordinates of the point of intersection. Step 4: Check the coordinates algebraically by substituting into each equation of the original linear system.

Solve the linear system by graphing. Check your solution. Ex.1: A linear system that has exactly one solution is called a consistent independent system because the lines are distinct (are independent) and intersect (are consistent).

Why is it a good idea to check a solution algebraically? An algebraic check confirms that you read the point of intersection correctly. Solve the linear system by graphing. Check your solution. Ex.2:

Ex.3: Ex.4: Ex.5: A business rents in-line skates and bicycles. The cost of renting skates is $15 per day and the cost of renting bicycles is $30 per day. During one day, the business has a total of 25 rentals and collects $450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented.