Question

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Answer 1

@jim_thompson5910

Answer 2

I was incorrect, here is the prompt:

Solve using matrices.
4x + 5y = 40
x – y = 1

Show work for full credit.

Answer 3

And here is what I wrote:

(1) Write the equations in matrix form, resulting in:

| 4 5 | * | x | = | 40 |
| 1 -1 | | y | | 1 |

(2) Find the inverse of the coefficient matrix (which involves 1 / determinant, multiplying and subtracting the diagonals, which in this case is 1/(4*-1 - 5*1)), which results in:

1
------------
4*-1-5*1

multiplied by:

| -1 -5 |
| -1 4 |


(3) This results in:

-1/9

multiplied by:

| -1 -5 |
| -1 4 |


(4) Next, I multiplied both sides of the original matrix equation by the inverse matrix we just found:



-1/9 * | -1 -5 | | 4 5 | * | x | = | 40 | | -1 -5 | * -1/9
| -1 4 | | 1 -1 | | y | | 1 | | -1 4 |


Which after being simplified equals:

| 1 0 | . | x | = | 5 |
| 0 1 | | y | | 4 |

Which means that the answer is: 5, 4

@jim_thompson5910

Answer 4

your possible answer is (x,y) = (5,4)

so x = 5 and y = 4

Answer 5

go back to the original equations

4x + 5y = 40
x – y = 1

and plug those x & y values in. If you get 2 true equations, then the possible answer is indeed a true solution. BOTH equations must be true for it to work. If one isn't true, then the ordered pair isn't a solution.

Answer 6

refresh the page if you get a weird looking symbol

Answer 7

It's correct, then! @jim_thompson5910 Right?

Answer 8

yes you should get 2 true equations when you substitute x = 5 and y = 4