Question

Solve the system y = 2x + 6 and 3y = 6x + 18 by using graph paper or graphing technology. What is the solution to the system?

(2, 6)

(3, 6)

No Solutions

Infinite Solutions

Answer 1

The system has infinite solutions

Explanation:

we have

`y=2x+6` ----> equation A

`3y=6x+18` ----> equation B

Multiply by
`3` equation A

`3y=3*(2x+6)` ----->
`3y=6x+18` -----> equation C

equation C and equation B are the same line

The system of equations is a consistent dependent system

The system has infinite solutions

Answer 2

y = 2x + 6

3y = 6x + 18 or y = 2x + 6

so the graph of the two lines are the same

consequently, they system has
Infinite Solutions