4x-2y=3
6x-3y=5

Use matrix method to examine the following system of equations for consistency or inconsistency 4x-2y=3 and 6x-3y=5

2x-y=1 ; 6x+3y=5

4x-3y=8, 6x-y=29/3

Show that each of the following systems of linear equations is consistent and also find their solutions: 6x+4y=2 9x+6y=3 2x+3y=5 6x+9y=15 5x+3y+7z=4 3x+26 y+2z=9 7x+2y+10 z=5 x-y+z=3 2x+y-z=2 -x-2y+2z=1 x+y+z=6 x+2y+3z=14 x+4y+7z=30 2x+2y-2z=1 4x+4y-z=2 6x+6y+2z=3

Solve the following system of equations by matrix method : 5x+7y+2=0 4x+6y+3=0 5x+2y=3 3x+2y=5 3x+4y-5=0 x-y+3=0 3x+y=19 3x-y=23 3x+7y=4 x+2y=-1 3x+y=7 5x+3y=12

If the distance of line 2x-y+3=0 from 4x-2y+p=0 and 6x-3y+r=0 is respectively 1/sqrt(5) and 2/sqrt(5)

The equations of sides of a triangle are x+3y=0 , 4x-3y=5 and 3x-y=0. Then the line 6x-7y=0 passes through the __________ of the triangle.

Prove that the following lines are concurrent. (i)5x-3y=1 , 2x+3y=23 , 42x+21y=257 (ii) 2x+3y-4=0 , x-5y+7=0 , 6x-17y+24=0

Solve for x and y : 3x-2y=4 and 6x-4y=8

4x+3y=5, 2x-y=2