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The cost of bowling at bowling alley A or B is a function of the number of games g. Cost A = 2.5g + 2 Cost B = 2g + 4 When are the costs the same? UNIT QUESTION: How do I justify and solve the solution to a system of equations or inequalities? Standard: MCC9-12.A.REI.1, 3, 5, 6, and 12 Learning Target: Students can find the solution to a system of equations by graphing. Standard: MCC9-12.A.REI.6 The lines can intersect The lines can be parallel (same slope) The lines can coincide (one on top of the other) • A consistent system is a system that has at least one solution. • An inconsistent system has no solution. • An independent system has EXACTLY one solution. • A dependent system has infinite solutions. Consistent Independent Inconsistent Consistent Dependent There are 3 different types of systems of linear equations 3 Different Systems: 1) Consistent-independent 2) Consistent-dependent 3) Inconsistent 1. 2. 3. Make sure each equation is in slope-intercept form: y = mx + b. Graph each equation on the same graph paper. The point where the lines intersect is the solution. (If they don’t intersect then there’s no solution. If the lines are the same, there are infinite solutions) 4. Check your solution algebraically. 𝒚 = 𝟑𝒙 − 𝟏𝟐 𝒚 = −𝟐𝒙 + 𝟑 Solution: (3, -3) 2𝑥 − 2𝑦 = −8 2𝑥 + 2𝑦 = 4 Solution: (-1, 3) 𝑦 = −2𝑥 + 5 𝑦 = −2𝑥 + 1 No Solution 2𝑦 = 4𝑥 + 6 −8𝑥 + 4𝑦 = 12 Infinite Solutions 𝑦=5 𝑥 = −2 Solution: (-2, 5) If the lines have the same y-intercept b, and the same slope m, then the system is consistentdependent If the lines have the same slope m, but different yintercepts b, the system is inconsistent If the lines have different slopes m, the system is consistent-independent Guided Practice 1-30. Questions *Even #’s Only*