TWOVARIABLE SYSTEMS OF EQUATIONS SKILL 13 BELL RINGER

TWO-VARIABLE SYSTEMS OF EQUATIONS SKILL 13

BELL RINGER •

OBJECTIVES • Understand how to graph systems of equations • Solve linear systems using elimination • Solve linear systems using substitution

INTRO. GRAPHING SYSTEMS OF EQUATIONS • We can obtain the solution of linear equations by plotting graphs of both equations. • The point of intersection will be the solution of the given system of equations. • Graph of a linear equation exhibits a straight line. • For parallel lines, there is no point of intersection, hence solution doesn’t exist. • The solution of systems of linear equations is correct if it satisfies the given equations.

EXAMPLE: GRAPH THE SYSTEM OF EQUATIONS

INTRO. SOLVING SYSTEMS ALGEBRAICALLY • System of equations - is a system having more than one equation. • System of simultaneous equations - a group of equations that must be all true at the same time. • Solution of equation - values which satisfy the given system of equations

EXAMPLE: SOLVE THE SYSTEM OF EQUATIONS

EXAMPLE: SOLVE THE SYSTEM OF EQUATIONS

EXAMPLE: SOLVE THE SYSTEM OF EQUATIONS

EXAMPLE: MIXTURE APPLICATION PROBLEM Suppose you work in a lab. You need a 15% acid solution, but your supplier only ships a 10% solution and a 30% solution. Rather than pay the hefty surcharge to have the supplier make a 15% solution, you decide to mix 10% solution with 30% solution, to make your own 15% solution. You need 10 liters of the 15% acid solution. How many liters of 10% solution and 30% solution should you use?

EXAMPLE: RATE-DISTANCE APPLICATION PROBLEM Two cyclists start at the same corner and ride in opposite directions. One cyclist rides twice as fast as the other. In 3 hours, they are 81 miles apart. Find the rate of each cyclist.

EXAMPLE: BREAK-EVEN APPLICATION PROBLEM A company makes and sells flash drives. The cost of producing each flash drive is $5. 00 and the fixed cost of $15, 000 per year. The company plans to sell the drives at $10. 00 apiece. How many flash drives must be sold to break even?

BELL RINGER • WHAT IS THE RATE-DISTANCE EQUATION? _______________ • WHAT IS THE BREAK-EVEN EQUATION? _________________ • DESCRIBE HOW TO SET UP A MIXTURE PROBLEM______________________________

EXAMPLE: RATE-DISTANCE APPLICATION PROBLEM An airplane is flying into a headwind travels a 2000 mile distance between Cleveland Fresno in 4 hours and 24 minutes The return flight takes 4 hours. Find the plane speed and wind speed.

EXAMPLE: MIXTURE APPLICATION PROBLEM To build the garden of your dreams you need 10 ft³ of soil containing 17% clay. You have two types of soil you can combine to achieve this: soil with 35% clay and soil with 10% clay. How much of each soil should you use?

EXAMPLE: BREAK-EVEN APPLICATION PROBLEM A business invests $12, 000 to produce a new product. Each unit costs $0. 85 to make. Each is sold for $2. 25. Find the number of units to break-even.