2.1 Solving Systems of Equations

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Presentation transcript:

2.1 Solving Systems of Equations Objectives: Solve systems of equations graphically and algebraically.

A set of two or more equations. Systems of Equations: A set of two or more equations. Solution: The intersection of the graphs Ex. 1) Solve the system of equations by graphing. y = 4x – 18 y = ¾x - 5

Consistent: A system of equations that has at least one solution. Inconsistent: A system of equations that has no solutions. (parallel lines) Independent: A system of equations that has exactly one solution. Dependent: A system of equations that has infinitely many solutions. (same lines…coincide)

See page 68 Elimination & Substitution: Algebraic methods to solve a system of equations. Ex. 2) Use elimination to solve: 5x + 2y = 340 3x – 4y = 360 Ex. 3) Use substitution to solve: y = 3x - 8 2x + y = 22

Ex. 4.) The Cotton Club, a manufacturer of sweatshirts, has fixed costs of $2000 and a variable cost of $5.00 per sweatshirt. It sells sweatshirts for $15.00 each. a.) Find the break-even point. b.) What is the least number of sweatshirts the Cotton Club must sell to make a profit?