Solving Systems Using Tables and Graphs Solving Systems

Solving Systems Using Tables and Graphs. Solving Systems Algebraically. n r a e l l l ’ u yo t a Wh To solve linear system using a graph or a table To solve linear systems algebraically. To solve Real world problems involving systems of linear equations in two variables y r a l u b a Voc System of equations, linear system, solution of a system, inconsistent system, independent system, dependent system

Using a graph or table What is the solution of the system? -3 x+2 y=8 Method 1: Graph both equations x+2 y=-8 When x=0 -3(0)+2 y=8 y=4 (0, 4) 0+2 y=-8 y=-4 (0, -4) When y=0 x+2(0)=-8 -3 x+2(0)=8 x=-8 -3 x=8 (-8, 0) =-2. 7 The point of intersection is (-4, -2) (-2. 7, 0) To verify check by substituting the point in both equations and get a true statement

Your turn What is the solution of the system? X-2 y=4 3 x+y=5 x=0 0 -2 y=4 y=-2 (0, -2) Y=0 X-2(0)=4 x=4 (4, 0) The solution is (2, -1) x=0 3(0)+y=5 (0, 5) y=0 3 x+0=5 3 x=5 x=1. 7 (5/3, 0)

Just a note When you have two or more related unknowns, you may be able to represent their relationship with a system of equationsa set of two or more equations A linear system consists of linear equations. A solution of a system is a set of values for the variables that makes all equations true You can classify a system of two linear equations by the number of solutions One solution consistent independent Infinitely many solutions consistent dependent No solution inconsistent

Remember and fill the blank. slope and _______ different y-intercept *Parallel lines have same ____ equal and the y-intercept *Slope of coincides lines are _____ same is the ______ Ax+By=C *For linear system in the standard form (_____) if the equations are linear _____ of each other multiples inconsistent then the system is _______ *If they are the same linear multiples but the constant are ______ , then the system is _______ not inconsistent *If the coefficients are not of the same multiple, then the system is _______ independent *Different slope is a condition that indicates anindependent _______ system Slope, Ax+By=C, independent, different, multiples, independent, equal, same, different, not

One more time Independent Consistent System At least one solution Has one solution Dependent Has infinitely many solutions The two equations represents the same line Inconsistent System Has no solution The two equations represents parallel lines

Your turn: Classifying a System Without Graphing Without graphing is each system independent, or inconsistent A. Hint: rewrite in the slope intercept form y=4+3 x same slope y=-3+3 x diff. y-int. B. diff slope diff y-int. C. Answers A. Inconsistent B. Independent C. dependent y=2 x-3

Solving by Substitution Step 1: solve one of the Equations for one of the variables Step 3: Substitute the Value for x into one of the original equations Step 2: Substitute the expression for y in the other equation

Solving by Elimination Then substitute for y in any of the original equations

Solving by Equivalent Equations or Multiplication You will need the x-terms or the y-terms become the opposites to eliminate them Solution(-5, 2) Then substitute

Solve A music store offers piano lessons at a discount price for customers buying new pianos. What is the cost for each lesson and one time fee for materials. c: the cost of one lesson f: the one time fee Relate: You solve it c=30, f=120

Solve An online music store offers 15 downloads for $19. 75 and 40 downloads for $43. 50. Each price includes the Same one time registration fee. Answer: 15 d+f=19. 75 40 d+f=43. 50 d=0. 95 f=5. 50

Your turn You want to buy a camera. A film camera costs $89. 98, and each photo costs $0. 24. A digital camera costs $124. 48, and each photo costs $0. 09. After how many photos will the overall cost of the cameras be the same? What will that cost be? Answer: 0. 24 x+89. 98=y 0. 09 x+124. 48=y 0. 24 x+89. 98=0. 09 x+124. 48 After 230 photos and the cost is $145. 18 You are in charge of ordering labels for a small business. A company that makes custom labels charges a yearly fee plus a cost per label. You paid $375 last year for 300 labels. This year you ordered 1, 000 labels and paid $725. What are the yearly fee and cost per label, assuming the prices did not change? Answer: 300 x+f=375 $225 yearly fee; $0. 50 per label 1000 x+f=725

Classwork odd Homework even