Beyonce is solving a system of equations:
2x-3y=-2 and 4x+y=24
She multiplies the second equation by 3 and then adds the first equation to find 14x=-70, showing her that x=5. Beyonce finds that y=4. Thinking about this process, Beyonce says out loud,
“There are lots of ways I could go about solving this problem. I could do the method above or I could multiply the first equation by -2 and add the second. I seem to find that there is only one solution to the two equations but I wonder if I will get the same solution if I use a different method?
What is the answer to Beyonce's question? Be sure to show work or explain reasoning.

Is the answer to (a) different if we have a system of two equations with no solutions? What if there are infinite solutions?

Beyonce will get the same result.

Step-by-step explanation:

The given system is

2x-3y=-2

and 4

x+y=24

This system contains two lines that are not parallel to each other therefore the solution x=5, y=4 is unique.

It doesn't matter which method he used or which variable he eliminated first.

The solution will still be the same.

If the system of two equations with has no solution, the Beyonce will not get a solution in the first place, but the fact that the system has no solution remains the same even if Beyonce uses a different method.

If there are infinite solutions, Beyonce might get different solutions using a different method, but the fact that the system has infinite solution remains the same.

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)  

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3