Transcript Example: Equal Values Method

Solving a System of Equations
with the Equal Values Method
Example: Chubby Bunny
Barbara 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.
3x  5y  x  19
y  3x  5

x
x
3
x

5
3x  5
2x  5  19
Since we want
to know when
the weights (y)
are equal, the
right sides need
to be equal too.
7 years
5 5
2x  14
2 2
x7
(b) How much do the cat and bunny weigh at this
Substitute the x from (a) into an equation:
Both
equations
SHOULD
give you
the same
time? answer.
y3
19
y
7 75  26 pounds
Example: Equal Values Method
Solve the following system of equation algebraically:
Both equations equal
y. Set them equal to
each other.
y  2x  22
y  3 x  28
2x  22  3x  28
22  5x  28
50  5x
10  x
y  3 10  28
y  30  28
y2
10, 2
Writing a system of Equations
Elise 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?
b: Number of bottles Elise took to the recycling plant
c: Number of cans Elise took to the recycling plant
c

4
b

1
Equal Values
Solve the other
Method
equation for c too 0.12b  0.1c  2.18
0.12b  0.1c  2.18
21.8 1.2b  4b 1
0.12b
0.12b
0.1c  2.18  .12b  0.1
c  21.8 1.2b
4 bottles
4  4   1 17 cans
Bottles:
Cans:
1.2b 1.2b
21.8  5.2b  1
1
1
 20.8  5.2b  5.2
4b