Question

Prove that the lines 4x + 3y = 10, 3x–4y = –5 and 5x + y = 7 are concurrent.

Answer 1

To prove that the lines
4x+3y=10 ; 4x+3y-10=0
3x-4y=-5 ; 3x-4y+5=0
5x+1y=7 ; 5x+1y-7=0
Take determinant and prove it is equal to
4 3 -10
3 -4 5 = 4(28-5) -3(-21-25)-10(3+20)
5 1 -7
=4(23)-3(-46)-10(23)
=92+138-230
=230-230
=0
Since determinant is = 0
Therefore,the lines r concurrent