Graphical Solutions of Pair of Linear Equations in Two Variables

Since any point on the Y-axis is in the form (0, k), i.e., x coordinate is equal to zero.

So, 5x – y = 7 and 10x + y = 15
5(0) –(k) = 7 and 10(0) + (k) = 15
k = –7 and k = 15
Required coordinates are (0, –7) and (0, 15).

Here y = 0

2(x – 3) = 0 – 8

(x – 3) = –4

x = –1

Required coordinate = (–1, 0)

Since any point on the Y-axis is in the form (0, k), i.e., x coordinate is equal to zero.

So, 3x – y = 5 and 6x – y = 10

3(0) – y = 5 and 6(0) – y = 10

y = –5 and y = –10

Hence, required coordinates are (0, –5), (0, –10).

As parallel lines do not intersect each other. So, the equations have no common solution.

Consistency means the system of equations has at least one solution. Since B has infinitely many solutions, that system of equations is consistent.