Verified answer

This involves setting up and coefficient matrix and performing row operations. It's a bit of an involved process but here is a not-too-dense look at it:

http://www.sosmath.com/matrix/system1/system1.html

If this doesn't do it for you keep Googling, there are tons of resources on this out there.

It's not something that is really easily explained here in few sentences if you are unaware of what row operations are or how to set up the matrices and how to formulate your solution once the system is solved.

Edit: I took your question to mean you were looking for how to do it in general, if you wanted just the answer to the system you put up let me know so I'll just delete this.

Its quite easy:

First, you have to know how to multiply Matrices by Vectors

_ _ _

| A B | * | F | = | A*F + B*G |

| C D | * | G | = | C*F + D*G |

So a 2x2 Matrix Multiplied by a 2x1 Vector is a 2x1 Vector.

Then, our system is:

2x - 5y = -2

-3x + 1y = -10

Thats the same as writing:

| 2 -5 | * | x | = | -2 |

| -3 1 | * | y | = | -10 |

(Make the multiplication to verify it)

And theres a property of this linear equations that lets you do this extended matrix and simplify it with row operations:

2 -5 -2

-3 1 -10

So, pivot it until you get this matrix

1 0 A

0 1 B

x = A

y = B

Thats the answer. In this case it should be 4 and 2

Peace!

NOTE: The double * and = I put are there just because i cant put one in the middle, it doesnt mean you multiply it in both rows

enable C, R and D, respectively, be the style of Carnations, Roses and Daisies. (a million) Then, C + R + D = 2 hundred (2) when you consider that there are 20 greater daisies than roses, D = 20 + R (3) Combining (a million) and (2), we've C + R + (20 + R) = C + 2R + 20 = 2 hundred, so (4) C + 2R = one hundred eighty subsequent, (5) a million.5C + 5.75R + 2.6D = a million.5C + 5.75R + 2.6(20 + R) = 589.5; a million.5C + 5.75R + 2.6(20 + R) = a million.5C + 8.35R + fifty two = 589.5; so (6) a million.5C + 8.35R = 537.5 Now, with expressions (4) and (6), style matrices to resolve for C and R. There are 3 matrices to contemplate: M1, M2 and M3, as follows: (7) The determinant M1 contains row a million = (a million, 2) and row 2 = (a million.5, 8.35); Matrix M2 contains row a million = (one hundred eighty, 2) and row 2 = (537.5, 8.35); and Matrix M3 contains row a million = (a million, one hundred eighty) and row 2 = (a million.5, 537.5). Then, (8) C = M2/M1 and R = M3/M1 you ought to locate that C = 80 and R = 50, so D = 70.

✐Explanation✐

You are using Cramer's Rule!

2x - 5y = -2

-3x + y = -10

Determine each determinant: D, Dx, and Dy.

|2...-5|

|-3...1| = D

D = -(2)(1) + (-3)(-5) = -2 + 15 = 13

|-5...-2|

|1..-10| = Dx

Dx = (-5)(-10) - (1)(-2) = 50 + 2 = 52

|2....-2|

|-3.-10|

Dy = -(2)(-10) + (-3)(-2) = 20 + 6 = 26

Divide Dx by D and Dy by D.

Dx/D = 4

Dy/D = 2

x = 4 and y = 2