8-4 Using Systems of Equations Warm-up Problems1. Solve.

y = 3x – 2 2x +5y = 7

2. Solve.5x – 2y = 42x + 4y = 16

Chapter 88-4 Using Systems of Equations

Example 1• A baseball team played 162 games. They won 44

more games than they lost. How many games did they lose?Question: How many games did the team lose?Data: Total games played = 162; 44 more games were won than lost.

Let x = games won and y = games lost.

The # of games won plus the # of games lost is 162

x + y = 162

The # of games won minus the # of games lost is 44

x – y = 44

We solve the system of equations by the addition method.

x + y = 162x – y = 44

2x = 206 x = 103

x + y = 162 103 + y = 162

y = 59

The team won 103 games and lost 59 games.

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a. An automobile dealer sold 180 vans and trucks at a sale. He sold 40 more vans than trucks. How many of each did he sell?

Example 2

• Ramon sells cars and trucks. He has room on his lot for 510 vehicles. From experience he knows that his profits will be greatest if he has 190 more cars than trucks. How many of each vehicle does he have?Let x = the number of cars and y = the number of trucks.

# of cars plus # of trucks is 510

x + y = 510

# of cars is 190 plus number of trucks

x = 190 + y

We solve the substitution method to solve the system.

x + y = 510x = 190 + y

(190 + y) + y = 510190 + 2y = 510 2y = 320 y = 160

x + y = 510 x + 160 = 510

x = 350

Ramon has 350 cars and 160 trucks in his lot.

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b. A family went camping at a place 45 km from town. They drove 13 km more than they walked to get to the campsite. How far did they walk?

Example 3

• Shirley is 21 years older than Laura. In six years, Shirley will be twice as old as Laura. How old are they now? Let x = Shirley’s age and y = Laura’s age.

Age now Age in 6 years

Shirley

Laura

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c. Wilma is 13 years older than Bev. In nine years, Wilma will be twice as old as Bev. How old is Bev?

d. Stan is two thirds as old as Adam. In 7 years, Stan will be three fourths as old as Adam. How old are they now?

e. Four pencils and two pens cost $0.74. Six pencils and five pens cost $1.53. Find the cost of a pencil and a pen.

Example 4

• Badger Rent-A-Truck rents small trucks at a daily rate of $33.95 plus 30¢ per mile. Cactus Rent-A-Truck rents the same size truck at a daily rate of $32.95 plus 32¢ per mile. For what mileage is the cost the same?

Let m represent the mileage.Let c represent the cost.

Charge per mile

($)

Charge for m

miles ($)

Daily Rate ($)

Badger

Cactus

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f. Acme rents a pickup truck at a daily rate of $31.95 plus 33¢ per mile. Speedo Rentzit rents a pickup for $34.95 plus 29¢ per mile. For what mileage is the cost the same?