Question

22. If x can be any number, how many solutions are there for the equation?

y = 3x – 1

A.
There is no solution because there are no values for the variables that make the equation true.

B.
There are two solutions because there are two variables in the equation.

C.
There is only one solution because all equations have one solution.

D.
There are many solutions because there are many values for the variables that make the equation true.

@jim_thompson5910

Answer 1

@Ciarán95

Answer 2

Im thinking D

Answer 3

What is one solution you can find? A solution would be in the form (x,y)

Answer 4

Oh, (3,8)

Answer 5

good, what's another?

Answer 6

(1, 0)

Answer 7

y = 3x – 1
y = 3*1 – 1 ... plug in x = 1
y = 3-1
y = 2

So the ordered pair is actually (1,2)

Answer 8

ohh sorry

Answer 9

what do you get when you plug in say x = 0

Answer 10

(0, -1)

Answer 11

so far you have these three solutions
(0,-1)
(1,2)
(3,8)
as you can see there are infinitely more because you can plug in any x value to get a corresponding y value. There are no limits or restrictions for x

Answer 12

Oh okay! so D!

Answer 13

correct

Answer 14

Yay! Thank you!

Answer 15

\[y = 3x - 1\]

We know that our x can be any value. We're going to fix a particular value for y, say y = 0.

\[1 = 3x - 1\]

For this equation to hold, we can let x = 1/3, as:
\[0 = 3(\frac{ 1 }{ 3 }) - 1 = 1 - 1 = 0\]

Similarly, if we set y = 2, then:
\[2 = 3x - 1\]
For this equation to hold, we let x = 1, as:
\[2 = 3(1) - 1 = 3 - 1 = 2\]


So, it doesn't matter what we define to be our y-value, we can always find a value for x to plug to so that the equation is satisfied, as the question tells us that x can be any value (positive , negative or a fraction).

Therefore, as @jim_thompson5910 explained, there will be infinitely many (x, y) pairs which we can plug in as solutions to our equation!

Answer 16

wow wow wow @Ciarán95 XD You are wooooooooow

Answer 17

Thank you so much @x__hazel__x :D