Graphing Linear Systems Math Tech II Everette Keller

Variables are unknown numbers in disguise represented by letters that are usually x or y.

y = 3x + 4

Two of more linear equations in the same variable form a system of linear equations, or simply a linear system.

y = 3x y = x + 4

A solution of a linear system in two variables is a pair of numbers a and b for which x = a and y = b make each equation a true statement. Such a solution can be written as an ordered pair (a,b) in which a and b are the values of x and y that solve the linear system. The point (a,b) that lies of the graph of each equation is called point of intersection of the graphs.

Find the solution to the linear system by graphing 3x + 2y = 4 -x + 3y = -5

Step 1 – Write each equation in a form that is easy to graph Step 2 – Graph both equations in the same coordinate plane Step 3 – Estimate the coordinates of the point of intersection Step 4 – Check whether the coordinates give a solution by substituting them into each equation of the original linear system.

Find the solution to the linear system by graphing x + y = -2 2x – 3y = -9

Find the solution to the linear system by graphing 3x - 2y = 11 -x + 6y = 7

Find the solution to the linear system by graphing x + 3y = 15 4x + y = 6

Find the solution to the linear system by graphing -15x + 7y = 1 3x – y = 1

1.What is the independent and dependent variables mean in a linear function? 2.What makes the equation have a linear relationship? 3.Explain to me what a system of linear equations is 4.What does it mean for the lines to linear functions in a system to intersect?

What are the benefits and limitations of solving linear systems through graphing?

Find a real life problem that relates to solving linear systems by graphing and state it for the next class period Problems 1 – 10 on the Handout