Algebra 1 Common Core Student Edition, Grade 8-9

Think
Is th e r e a n o th e r
way to solve this
problem?
Yes. You can make a
table. Show the weight
of each alligator after
1 month, 2 months, and
so on.

S$ Got It? 1. W hat is the solution of the system? Use a graph. y = 2x + 4

Check your answer. y = x + 2

Pr o b l em 2 Writ ing a Syst em of Equat ions 63S)

Biology Scientists studied the weights of two alligators over a period of 12 months.

The initial weight and growth rate of each alligator are shown below. After how many

months did the alligators weigh the same amount?

Let w = alligator weight.

Let t = tim e in m onths.

Write Alligator 1: w = 4 + 1.5 • f

Alligator 2: w = 6 + 1 • t

G raph b o th equations in th e sam e coordinate plane.

w = 4 + 1.5f The s lo p e is 1 .5. The w - in t e r c e p t is 4.

w = 6 + t The s lo p e is 1. The w - in t e r c e p t is 6.

The lines intersect at (4,10).

After 4 m onths, b o th alligators w eighed 10 lb.

& Got It? 2. One satellite radio service charges $10 p e r m o n th plus

an activation fee of $20. A seco n d service charges $11 p er

m o n th plus an activation fee of $15. In w h at m o n th was

th e cost of th e service th e sam e?

£

¥

CT)

'3

Time, t (months)

A system of equations th a t has at least one solution is consistent. A c o n s is te n t system

can be either independent o r dependent.

A consistent system th a t is in d e p e n d e n t h as exactly one solution. For example, the

system s in Problem s 1 a n d 2 are consistent a n d in d ep en d e n t. A consistent system that

is dependent has infinitely m an y solutions.

A system of equations th a t has no solution is in c o n s is te n t.

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Lesso n 6- 1 So l vi n g Syst em s b y Gr ap h i n g 365