Question

How many solutions does the system have? y = -2x-4 \\\\ y = 3x+3

Answer 1

The system has one solution.

Explanation:

We have two equations:

y = -2x - 4

y = 3x + 3

Equalling them:

y = y

-2x - 4 = 3x + 3

5x = -7

`x = -(7)/(5)`

And

`y = 3x + 3 = 3(-(7)/(5)) + 3 = (-21)/(5) + 3 = (-21)/(5) + (15)/(5) = -(6)/(5)`

Replacing in the other equation we should get the same result.

`y = -2x - 4 = -2(-(7)/(5)) - 4 = \frac{14}[5} - 4 = (14)/(4) - (20)/(5) = -(6)/(5)`

So the system has one solution.