A day full of math games & activities. Find one near you.

For all real values of c, the pair of equations x - 2y = 8; 5x - 10y = c have a unique solution. Justify whether it is true or false

Solution:

Given, the pair of linear equations is

x - 2y = 8

5x - 10y = c

We have to find the value of c so that the equations have a unique solution.

For a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,

if \(\frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}}\), then the graph will be a pair of lines intersecting at a unique point, which is the solution of the pair of equations.

Here, a₁ = 1, b₁ = -2, c₁= 8

a₂ = 5, b₂ = -10, c₂ = c

So, a₁/a₂ = 1/5

b₁/b₂ = -2/-10 = 1/5

c₁/c₂ = 8/c

1/5 = 1/5 = 8/c

So, 1/5 = 8/c

c = 8(5)

c = 40

At c = 40, \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\), the pair of equations have infinitely many solutions.

Therefore, for all real values of c, the pair of equations x - 2y = 8; 5x - 10y = c does not have a unique solution.

✦ Try This: For all real values of c, the pair of equations x + 2y = 8; 4x + 8y = c have a unique solution. Justify whether it is true or false

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.2 Problem 5

For all real values of c, the pair of equations x - 2y = 8; 5x - 10y = c have a unique solution. Justify whether it is true or false

Summary:

For all real values of c, the pair of equations x - 2y = 8; 5x - 10y = c have a unique solution. The statement is false

☛ Related Questions: