How many solutions does this system have? x minus y = negative 4. 3 x + y = 8. one two an infinite number no solution

The correct answer is A.) one

Step-by-step explanation:

I just did the test on edge 2021 and got it right!

(a) B

(b) $2

Step-by-step explanation:

(a) Let's say the cost of a ticket is t and the cost of popcorn is p. Then we can write the two equations from the table:

12t + 8p = 184

9t + 6p = 138

We need to solve this, so let's use elimination. Multiply the first equation by 3 and the second equation by 4:

3 * (12t + 8p = 184)

4 * (9t + 6p = 138)

We get:

36t + 24p = 552

36t + 24p = 552

Subtract the second from the first:

    36t + 24p = 552

-    36t + 24p = 552

       0 = 0

Since we get down to 0 = 0, which is always true, we know that we cannot determine the cost of each ticket because there is more than one solution (infinitely many, actually). The answer is B.

(b) Our equation from this, if we still use t and p, is:

5t + 4p = 82

Now, just choose any of the two equations from above. Let's just pick 9t + 6p = 138. Now, we have the system:

5t + 4p = 82

9t + 6p = 138

To solve, let's use elimination again. Multiply the first equation by 6 and the second one by 4:

6 * (5t + 4p = 82)

4 * (9t + 6p = 138)

We get:

30t + 24p = 492

36t + 24p = 552

Subtract the second from the first:

    36t + 24p = 552

-    30t + 24p = 492

      6t + 0p = 60

So, t = 60/6 = $10. Plug this back into any of the equations to solve for p:

5t + 4p = 82

5 * 10 + 4p = 82

50 + 4p = 82

4p = 32

p = 32/4 = $8

So the ticket costs 10 - 8 = $2 more dollars than the popcorn.