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Solving Systems of Equations and Inequalities by Graphing

In this tutorial, learn how to solve systems of equations and inequalities algebraically and graphically. By rewriting equations in slope-intercept form (y = mx + b) and graphing them, you can visually identify solutions. Highlight the first equation with a solid line since it includes an equality. Choose a test point to determine shading for inequalities, ensuring accurate representation of the solution area. Progress through example problems and prepare for homework on graph paper. Practice further with elimination and substitution techniques for quizzes.

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Solving Systems of Equations and Inequalities by Graphing

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  1. Warm - Up • Solve the system algebraically: x + ½y = 5 3y – 2x = 6

  2. Chapter 3.3 Solving Systems of Inequalities by Graphing

  3. Solve a system of inequalities by graphing: Just like before, in order to graph – you must first rewrite the equations in slope-intercept form Y=mx + b

  4. Graph the first equation • The first equation is already in slope-intercept form. • Remember that the line must be solid since the inequality is also equal to • Then pick a test point: For example, choose (0,0) since it is not on the line itself. Substitute in for (x,y) • 0≥3(0)-2 0≥-2 ? Yes

  5. Graph first equation on graph and shade

  6. Rewrite Second Equation • 2x – 4y < 12 • - 4y < - 2x + 12 • y > ½ x - 3 • Pick test point to see what side is shaded.

  7. Graph the second equation on the same graph as the first The solutions lie within the area where the two shadings overlap

  8. You Try! First: Rewrite the equations Second: Graph the equations Third: Pick a point to decide the shading

  9. Tonight’s Homework: Page 126 (12-19) ON GRAPH PAPER Quiz – Elimination/Substitution Next Class

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