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9/28/09 (Monday) NOTES CLASSWORK HOMEWORK System of Equations A set of equations for which a common solution is sought A solution of two equations in two variables is an ordered pair that makes both equations true. CW on Graphing Linear Inequalities Hw#61 TB p. 338 #27-30 There are three ways to solve a system of equations. 1) Graphing (the point of intersection is the solution of the system) - If lines have one point of intersection, that’s the only solution of the system.(consistent and independent) - If the lines are parallel, there’s no solution.(inconsistent) - If the lines coincide, there’s an infinite number of solutions.(consistent and dependent) 2) Substitution Method 3) Addition (Elimination) Method S.N PH p. 419 #27-30 p. 420 #35-40 Graph on a coordinate plane. 27) 5 x 4 y 20 28) y 1 2 x 29) y 2 x 1 30) y 4 x 0 Write an inequality for each graph.(You need the textbook for these problems because there are graphs you need to see.) 35) (There is a dashed line going through 1 on the y-axis and the slope is 1. The right half plane is shaded) 36) (A solid line goes through -4 on the y-axis and the slope is 1. Right side is shaded) 37) (A dashed line goes through -2 on the y-axis and the slope is 1. The left half plane is shaded) 38) (A solid line goes through 4 on the y-axis and the slope is 1. The left half plane is shaded) 39) (A solid line goes through -3 on the y-axis and the slope is 1. The right half plane is shaded) 40) (A vertical dashed line passes through -2 on the x-axis. The right half plane is shaded) Match each inequality with its graph. (You need to look at the textbook to do these problems for there are graphs to look at.) 27) 2y + x 6 1 x y 4 2 1 29) y 3 x 2 30) 4 y 2 x 16 28) 9/29/09 (Tuesday) NOTES CLASSWORK HOMEWORK System of Equations A set of equations for which a common solution is sought A solution of two equations in two variables is an ordered pair that makes both equations true. CW on Systems of Equations Hw#62 TB p. 339 #48-50 There are three ways to solve a system of equations. 1) Graphing (the point of intersection is the solution of the system) - If lines have one point of intersection, that’s the only solution of the system.(consistent and independent) - If the lines are parallel, there’s no solution.(inconsistent) - If the lines coincide, there’s an infinite number of solutions.(consistent and dependent) 2) Substitution Method 3) Addition (Elimination) Method S.N PH p. 360 #1-5, 9-12 Determine whether the given ordered pair is a solution of the system of equations. 1) (3,2); 2x + 3y = 12 x - 4y = -5 2) (1,5); 5x - 2y = -5 3x - 7y = -32 3) (3,2); 3t – 2s = 0 t + 2s = 15 4) (2,-2); b + 2a = 2 b – a = -4 5) (-1,1); x = -1 x – y = -2 Solve by Graphing. 9) x + y = 3, x – y = 1 10) x – y = 2, x + y = 6 11) x + 2y = 10, 3x + 4y = 8 12) -3x = 5 – y , 2y = 6x + 10 Write an equation in slope-intercept from of the line that passes through the given point and is parallel to the graph of each equation. 48) (1,-3); y = 3x – 2 49) (0,4); x + y = -3 50) (-1,2); 2x – y = 1 9/30/09 (Wednesday) NOTES CLASSWORK HOMEWORK Solving Systems of Equations Using the Substitution Method 1) Solve one of the equations for one of the variables (x=something or y=something) 2) Substitute what you solved for in step 1 in the second equation. 3) Solve the equation (you should have only one variable now). 4) Substitute that value into either of the original equations to find the other value. 5) Check your solution. CW on Systems of Equations Hw#63 TB p. 255 #1-4 9/30/09 (Wednesday) S.N PH p. 362 Try this #a-c, p.365 #1-4 NOTES CLASSWORK HOMEWORK Solving Systems of Equations Using the Substitution Method 1) Solve one of the equations for one of the variables (x=something or y=something) 2) Substitute what you solved for in step 1 in the second equation. 3) Solve the equation (you should have only one variable now). 4) Substitute that value into either of the original equations to find the other value. 5) Check your solution. CW on Systems of Equations Hw#63 TB p. S.N PH p.