Question

Solve the following system of equations graphically:

2x – y – 2 = 0

– 4x + y + 4 = 0

Also, find the absolute difference between the ordinates of the points where given lines cut y-axis.

Answer 1

To solve the system graphically, we find at least two coordinate points for each linear equation to plot them on the Cartesian plane. 

1. Line 1: 2x – y – 2 = 0

⇒ y = 2x – 2 

When x = 0: y = 2(0) – 2 = –2 

⇒ (0, –2) 

When x = 1: y = 2(1) – 2 = 0

⇒ (1, 0) 

2. Line 2: –4x + y + 4 = 0

⇒ y = 4x – 4

When x = 0: y = 4(0) – 4 = – 4 

⇒ (0, – 4)

When x = 1: y = 4(1) – 4 = 0 

⇒ (1, 0)

Both lines intersect perfectly at the point (1, 0), which provides the exact solution to the system.