1 / 7

Solve Systems of Equations & Graph Inequalities

Solve Systems of Equations & Graph Inequalities. Lesson 13.3 & 13.4. When two lines are graphed on the same coordinate plane, the lines may be:. Parallel Intersecting Identical (coincident). Two methods to solve a system of Equations:. Substitution: Substitute one equation into the other.

wyman
Download Presentation

Solve Systems of Equations & Graph Inequalities

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Solve Systems of Equations & Graph Inequalities Lesson 13.3 & 13.4

  2. When two lines are graphed on the same coordinate plane, the lines may be: • Parallel • Intersecting • Identical (coincident)

  3. Two methods to solve a system of Equations: • Substitution: • Substitute one equation into the other. • Find the intersection of the lines x = 4 and y = 2x + 8 • Substitute 4: y = 2(4) + 8 • y = 8 + 8 • y = 16 • The lines intersect at (4, 16)

  4. Two methods to solve a system of Equations: • Linear Combinations: • Add the two equations together to cancel out one of the variables. • Find the intersection of the lines 8x – 3y = 7 and 10x + 4y = 1 • Multiply the first equation by 4 and the second equation by 3. • 32x – 12y = 2830x + 12y = 3 • 62x = 31 • x = ½ Substitute ½ into one of the equations for x and solve for y. 8(1/2) – 3y = 7 -3y = 3 y = -1 The lines intersect at (1/2 , -1)

  5. Graph Inequalities • How to graph inequalities and system of inequalities: • Step 1: Pretend the inequality is an equation. Graph it the way you normally do. If the inequality is < or > use a dashed line. If it is ≤ or ≥ use a solid line. • Step 2: Use the inequality to test a point to find out which region to shade.

  6. Graph y > 2x - 4 • Graph the line as if it were an equation. Use a dashed line because it is >. • Use a test point to see where to shade. • 0 > 2(0) – 4 • 0 > -4 • True, shade where (0, 0) is.

  7. Determine the solution set of the system by graphing: • y ≤ 2/5x + 4y ≥ -½x + 42x + y ≤ 8 • Graph the 3 lines. • Test an ordered pair.(1, 4) • 4 ≤ 2/5(1) + 44 ≤ 42/5 True • 4 ≥ -½(1) + 4 4 ≥ 3½ True • 2(1) + 4 ≤ 86 ≤ 8 True • Shade where (1, 4) is.

More Related