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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.

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Solve Systems of Equations & Graph Inequalities

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  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.

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