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Warm Up

Learn how to solve systems of equations by graphing. Understand the different possibilities of solutions and how to check your answers.

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Warm Up

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  1. Warm Up • Is the ordered pair a solution to the equation 2x – 3y = 5? • (1,0) • (-1,1) • (1, -1) • (4,1)

  2. Warm Up Answers • Is the ordered pair a solution to the equation 2x – 3y = 5? • (1,0) no • (-1,1) no • (1, -1) yes • (4,1) yes

  3. Objective The student will be able to: solve systems of equations by graphing Designed by Skip Tyler, Varina High School Modified by Lisa Hoffmann Troy Buchanan High School

  4. What is a system of equations? • A system of equations is when you have two or more equations using the same variables. • The solution to the system is the point that satisfies ALL of the equations. This point will be an ordered pair. • When graphing, you will encounter three possibilities. • One, none, or many solutions

  5. Intersecting Lines • The point where the lines intersect is your solution. • The solution of this graph is (1, 2) (1,2)

  6. Parallel Lines • These lines never intersect! • Since the lines never cross, there is NO SOLUTION! • Parallel lines have the same slope with different y-intercepts.

  7. Coinciding Lines • These lines are the same! • Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS! • Coinciding lines have the same slope and y-intercepts.

  8. What is the solution of the system graphed below? • (2, -2) • (-2, 2) • No solution • Infinitely many solutions

  9. 1) Find the solution to the following system: 2x + y = 4 x - y = 2 Graph both equations. I will graph using x- and y-intercepts (plug in zeros or cover up method). Graph the ordered pairs. 2x + y = 4 (0, 4) and (2, 0) x – y = 2 (0, -2) and (2, 0)

  10. Graph the equations. 2x + y = 4 (0, 4) and (2, 0) x - y = 2 (0, -2) and (2, 0) Where do the lines intersect? (2, 0) 2x + y = 4 x – y = 2

  11. Check your answer! To check your answer, plug the point back into both equations. 2x + y = 4 2(2) + (0) = 4 x - y = 2 (2) – (0) = 2 Nice job…let’s try another!

  12. 2) Find the solution to the following system: y = 2x – 3 -2x + y = 1 Graph both equations. Put both equations in slope-intercept or standard form. I’ll do slope-intercept form on this one! y = 2x – 3 y = 2x + 1 Graph using slope and y-intercept

  13. Graph the equations. y = 2x – 3 m = 2 and b = -3 y = 2x + 1 m = 2 and b = 1 Where do the lines intersect? No solution! Notice that the slopes are the same with different y-intercepts. If you recognize this early, you don’t have to graph them!

  14. Check your answer! Not a lot to check…Just make sure you set up your equations correctly. I double-checked it and I did it right…

  15. What is the solution of this system? • (3, 1) • (4, 4) • No solution • Infinitely many solutions 3x – y = 8 2y = 6x -16

  16. Solving a system of equations by graphing. Let's summarize! There are 3 steps to solving a system using a graph. Graph using slope and y – intercept or x- and y-intercepts. Be sure to use a ruler and graph paper! Step 1: Graph both equations. This is the solution! LABEL the solution! Step 2: Do the graphs intersect? Substitute the x and y values into both equations to verify the point is a solution to both equations. Step 3: Check your solution.

  17. Online Explanation • http://www.mathwarehouse.com/algebra/linear_equation/systems-of-equation/index.php

  18. Technology • Graphing Calculators are a great tool to help you graph tougher equations, but you MUST solve each equation for y first • There are also online tools and downloadable graphing calculators that you can use to help you solve systems or check your answer. • Graphing Calculator - http://www.mathworksheetsgo.com/tools/free-online-graphing-calculator.php

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