Matrix help please3?

Question

Solve using a matrix:

x - 2y = 6

4x - 3y = 4

Answer 1

Multiply the top eq. by -4

-4x +8y=-24
4x-3y=4
add up

5y=-20 y = -4..... x+8 = 6 .... x = -2

Answer 2

you can solve this by first making it a coefficient matrix and forming an augmented matrix.

1x -2y = 6
4x - 3y = 4

[ x y | b ]
[ x y | b ]

so the matrix will be

[ 1 -2 | 6 ]
[ 4 -3 | 4 ]

we can solve this by gaussian, gauss-jordan, LU factorization.

i will use gauss-jordan where you will make the left side of the matrix an identity so that the left side will be the values of x and y..


[ 1 -2 | 6 ]
[ 4 -3 | 4 ]

multiply row 1 with -4 and add it to row 4
note: row 1 will not be affected

[ 1 -2 | 6 ]
[ 0 5 | -20 ]

divide row 2 with 5.

[ 1 -2 | 6 ]
[ 0 1 | -4 ]

multiply 2 in row 2 and add to row 1
note:row 2 is un affected

[ 1 0 | -2 ]
[ 0 1 | -4 ]

therefore:

x = -2
y = -4

Answer 3

|1 -2| * | x | = | 6 |
|4 -3| . | y | . | 4 |
det of A ~> -3 + 8 = 5
|-3 2| (1/5) = A^-1
|-4 1|
|1/5 -2/5| = A^-1
|4/5 -3/5|
A^-1 * A * |x, y| = A^-1 * |6, 4|
| x | = | -2 |
| y | . |-4 |
(-2,-4)

Answer 4

www.quickmath.com should help
You should get an answer of (-2,-4)