Equal Values Method

Since we want to know when the weights (y) are equal, the

right sides need to be equal too.

Example: Chubby BunnyBarbara has a bunny that weighs 5 lbs and gains 3 lbs per

year. Her cat weighs 19 lbs and 1 lbs per year. (a) When will the bunny and cat weigh the same amount?

Write rules where x represents the number of years and y represents the weight of the animal.

3 5y x 19y x 3 5x 3 5x 3 5x

3 5x x x2 5 19x

5 52 14x

7x 2 27 years

(b) How much do the cat and bunny weigh at this time?Substitute the x from (a) into an equation: 3 7 5y 26 pounds19 7y

Both equations SHOULD give you the same answer.

Example: Equal Values Method

Solve the following system of equation algebraically:

2 22

3 28

y x

y x

22 3 822 xx 22 5 28x

50 5x10 x

3 10 28y 30 28y 2y

10,2

y

2 22x Both equations equal y. Set them equal to

each other.

Writing a system of EquationsElise took all of her cans and bottles from home to the recycling plant. The

number of cans was one more than four times the number of bottles. She earned 10¢ for each can and 12¢ for each bottle, and ended up earning $2.18 in all. How many cans and bottles did she recycle?

21.8 1.2 4 1b b

5.220.8 5.2b

21.8 5.2 1b 1 1

4 bBottles:

Cans: 4 4 1 174bottles

cans

b:Number of bottles Elise took to the recycling plant c:Number of cans Elise took to the recycling plant

4 1c b 0.12 0.1 2.18b c

0.12 0.1 2.18b c

0.1 2.18 .12c b 0.12b 0.12b

0.121.8 1.2c b

1.2b 1.2b

Solve the other equation for c too

Equal Values Method