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2x+3y=5,4x+ky=10 find the value of k …

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2x+3y=5,4x+ky=10 find the value of k by infinity many solution

Posted by Shubhham Modi 6 years, 4 months ago

CBSE > Class 10 > Mathematics

2 answers

Yogita Ingle 6 years, 4 months ago

Equation 1: 2x + 3y = 5

Equation 2: 4x + ky = 10
Both the equations are in the form of :

a₁x + b₁y = c₁ & a₂x + b₂y = c₂ where a₁ & a₂are the coefficients of x

b₁ & b₂ are the coefficients of y

c₁ & c₂ are the constants

For the system of linear equations to have infinitely many solutions we must have
a1/a2 = b1/b2 = c1/c2 ………(i)

According to the problem:

a1 = 2, a2 = 4, b1 = 3, b2 = k, c1 = 5, c2 = 10

Putting the above values in equation (i) and solving the extreme left and extreme right portion of the equality we get the value of a
2/4 = 3/k
⇒ 2k = 12 ⇒ k = 6

The value of k for which the system of equations has infinitely many solution is k = 6

Sandeep Yadav 6 years, 4 months ago

Given - infinitely many solution =2/4=3/k K=6

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