Drill Graph the linear equation. 1. y = -2x x + 3y = 9

Drill Graph the linear inequality. 1. 3x – 2y < x – y > 2

Algebra 1 Ch 7.1 – Solving Linear Systems by Graphing

Before we begin…  In previous chapters you learned how to transform and graph linear equations using slope-intercept…  In this chapter, we will use that information to solve systems of linear equations in two variables…  The solution to a system of linear equations is an ordered pair or pairs that make both statements true…  To be successful here it is important to lay out your work in a logical sequential manner and not skip any steps.

Process  The steps below are the process to solving a system of linear equations by graphing 1. Write each equation in slope-intercept form. 2. Graph both equations on the same coordinate plane 3. Determine the coordinates of the point of intersection 4. Check the coordinates algebraically by substituting them into each equation of the original system of linear equations. Note: In order for the ordered pair to be a solution, after substituting, BOTH equations MUST be a true statement!

Example #1  Solve the linear system graphically. Check your solution algebraically. x + y = -2 2x – 3y = -9  The first step is to write the equations in a format that is easy to graph…

Step 1 – Rewrite Equations x + y = -2 -x y = -x - 2 2x – 3y = -9 -2x - 3y = -2x – y = 2/3x + 2 m = -1 b = -2 m = 2/3 b = +2 Now that you have both equations in slope-intercept form, the next step is to graph the equations on the same coordinate plane and determine the point where the 2 lines intersect

y x Step 2 – Graph Equations y = -x - 2 m = -1, b = -2 m = 2/3, b = +2 y = 2/3x + 2 y = -x - 2 y = 2/3x + 2

Step 3 – Determine Intersection y x y = -x - 2 y = 2/3x + 2 After graphing, it appears that the 2 lines intersect at the point (-3, 1) The next step is to substitute this point into both equations and solve algebraically

Step 4 – Check Solution Algebraically x + y = = = - 2 √ 2x – 3y = -9 2(-3) – 3(1) = – 3 = = - 9 √ Substitute the Ordered pair (-3, 1) into each equation and solve algebraically. TRUE Because (-3, 1) is the solution to BOTH equations it is the solution of this system of linear equations

Your Turn  Determine if the ordered pair is a solution to the system of linear equations 1. 3x – 2y = 11 -x + 6y = 7(5, 2) 2. 6x – 3y = -15 2x + y = -3(-2,1) 3. x + 3y = 15 4x + y = 6(3, -6) 4. -5x + y = 19 x – 7y = 3(-4, -1) x + 7y = 1 3x – y = 1(3, 5)

Your Turn  Graph & check to solve the linear system 6. y = -x + 3 y = x y = 2x – 4 y = - ½ x x + 4y = 16 y = x + 6y = 15 -2x + 3y = /5x + 3/5y = 12/5 -1/5x + 3/5y = 6/5

Your Turn Solutions 1. Solution 2. Solution 3. Not a solution 4. Solution 5. Not a solution 6. (1, 2) 7. (2,0) 8. (16,-16) 9. (3,1) 10. (3,3)

Summary  A key tool in making learning effective is being able to summarize what you learned in a lesson in your own words…  In this lesson we talked about solving linear systems by graphing. Therefore, in your own words summarize this lesson in one paragraph…be sure to include key concepts that the lesson covered as well as any points that are still not clear to you…  If you wish, you can use an example to help summarize.  You will turn this summary in for an exit ticket grade.