Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions:
5x - 8y + 1 = 0 (1)
3x - 24/ 5y + 3/5 = 0 (2)

Solution:

Let the coefficients of equation (1) be a₁ ,b₁  and c_1, and the coefficients of equation (2) be a₂ ,b₂  and c₂

Multiply equation (2) by 5/ 3.

⇒ 5/ 3 (3x - 24/ 5y + 3/5 = 0)

⇒ 5x - 8y + 1 = 0

which is same as equation (1)

Thus, a1 / a2 = b1/ b2 = c1/ c2

The pair equations has coincident lines and infinitely many solutions

Graphical representation of the equation.

When x = 0; y = 0.125 and x = - 1; y = - 0.5

☛ Check: NCERT Solutions for Class 10 Maths Chapter 3

Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions: 5x - 8y + 1 = 0 (1) 3x - 24/ 5y + 3/5 = 0 (2)

Summary:

The pair of equations 5x - 8y + 1 = 0; 3x - 24/ 5y + 3/5 = 0 has coincident lines and thus has infinitely many solutions

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