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**Solve Systems of Equations & Graph Inequalities**

Lesson 13.3 & 13.4

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**When two lines are graphed on the same coordinate plane, the lines may be:**

Parallel Intersecting Identical (coincident)

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**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)

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**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 = x + 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)

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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.

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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.

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**Determine the solution set of the system by graphing:**

y ≤ 2/5x + 4 y ≥ -½x x + y ≤ 8 Graph the 3 lines. Test an ordered pair. (1, 4) 4 ≤ 2/5(1) ≤ 42/5 True 4 ≥ -½(1) ≥ 3½ True 2(1) + 4 ≤ 8 6 ≤ 8 True Shade where (1, 4) is.

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