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For what value of k, do the equations 3x - y + 8 = 0 and 6x - ky = -16 represent coincident lines
a. 1/2
b. -1/2
c. 2
d. -2

Solution:

Given, the pair of equations is

3x - y + 8 = 0

6x - ky = -16 represent coincident lines.

We have to find the value of k.

We know that,

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

If \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\), then the pair of linear equations is dependent and consistent.

Here, a₁ = 3, b₁ = -1, c₁ = 8

a₂ = 6, b₂ = -k, c₂ = 16

So, a₁/a₂ = 3/6 = 1/2

b₁/b₂ = -1/-k = 1/k

c₁/c₂ = 8/16 = 1/2

\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{2}\)

\(\frac{1}{k}=\frac{1}{2}\)

Therefore, the value of k is 2.

✦ Try This: For what value of k, do the equations x - y + 8 = 0 and 3x - ky = -24 represent

coincident lines?

Given, the pair of equations are

x - y + 8 = 0

3x - ky = -24 represent coincident lines.

We have to find the value of k.

Here, a₁ = 1, b₁ = -1, c₁= 8

a₂ = 3, b₂ = -k, c₂ = 24

So, a₁/a₂ = 1/3

b₁/b₂ = -1/-k = 1/k

c₁/c₂ = 8/24 = 1/3

\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{3}\)

\(\frac{1}{k}=\frac{1}{3}\)

Therefore, the value of k is 3

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

NCERT Exemplar Class 10 Maths Exercise 3.1 Problem 6

For what value of k, do the equations 3x - y + 8 = 0 and 6x - ky = -16 represent coincident lines?, a. ½, b. -½, c. 2 , d. -2

Summary:

For the value of k = 2, the equations 3x - y + 8 = 0 and 6x - ky = -16 represent coincident lines.

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