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CCGPS Coordinate Algebra 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 Today’s Question: When is it better to use substitution than elimination for solving systems? Standard: MCC9-12.A.REI.6 Warm-up Solve and graph each inequality 1. 7x < 21 2. 30 < 5k 3. -2n > -50 4. 𝑦 5 > -20 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. 4. Check your solution algebraically. 1 𝑦 = 𝑥+3 2 y= 3 𝑥 2 +1 Solution: (2, 4) 2 x 2 y 8 2 x 2y 4 Solution: (-1, 3) y 2 x 5 y 2 x 1 yes Solution x y 2 2 x 3 y 9 Solution: (-3, 1) y5 2x y 1 Solution: (-2, 5) 1) One solution 2) No solution 3) Infinitely many If the lines have the same y-intercept b, and the same slope m, then the system has infinitely many solutions. If the lines have the same slope m, but different y-intercepts b, the system has no solution. If the lines have different slopes m, the system has one solution. Warm-Up 9/20/13 Solve each equation for y. 1. 2x + 3y = 6 2. -5x + 4y = 8 3. 3x – 4y + 12 = 0 1. 2. 3. 4. 5. One equation will have either x or y by itself, or can be solved for x or y easily. Substitute the expression from Step 1 into the other equation and solve for the other variable. Substitute the value from Step 2 into the equation from Step 1 and solve. Your solution is the ordered pair formed by x & y. Check the solution in both of the original equations. 1. y 6 x 11 2 x 3y 7 2. 2 x 3 y 1 y x 1 3. y 3 x 5 5 x 4y 3 4. 3 x 3y 3 y 5 x 17 5. y 2 4 x 3y 18 6. y 5 x 7 3 x 2 y 12 Graphing and Substitution WS