Using the Matrix of the Equations to Find the Solution

Given the equations and their matrix.
                                                 3x + 4y = 10
                                                 2x + 5y = 9
To eliminate y from the equations, multiply the first equation by 5 and the second equation by 4 and the second equation by 4 to get
                                                 15x + 20y = 50
                                                 8x + 20y = 36
Now subtract the second equation from the first and replace the first by the result::
                                                 7x + 0y = 14
                                                 8x + 20y = 36
Divide the first equation by 7 to get the value of x:
                                                 1x + 0y = 2    (x = 2)
                                                 8x + 20y = 36
To get the value of y, multiply the first equation by 8, then subtract the resulting equation from the first and replace the second equation by the result:
                                                 1x + 0y = 2
                                                 0x + 20y = 20
Now divide the second equation by 20 to get:
                                                 1x + 0y = 2
                                                 0x + 1y = 1    (y=1)