Question

Show graphically that the system of equations x – 4y + 14 = 0; 3x + 2y – 14 = 0 is consistent with unique solution.

Answer 1

The given system of equations is

x – 4y + 14 = 0 ….(1)

3x + 2y – 14 = 0 ….(2)

`x – 4y + 14 = 0 ⇒ y = \frac { x + 14 }{ 4 }`

x	6	-2
y	5	3
Points	A	B

`3x + 2y – 14 = 0 ⇒ y = \frac { -3x + 14 }{ 2 }`

x	0	4
y	7	1
Points	C	D

The given equations representing two lines, intersect each other at a unique point (2, 4). Hence, the equations are consistent with unique solution.