Question

If (2k -1, k) is a solution of the equation 10x−9y=12, then k is equal to :
A. 1
B. 2
C. 3
D. 4

Answer 1

Hint:The given question is in linear equation with two variables.Its solution pair is having values in a common variable K. First substitute the solution values in the given equation. Then solve the new linear equation in a single variable.

Complete step-by-step answer:
Linear equation is an equation with variables having highest power 1. In other words, the expression of equality of two algebraic expressions involving one or more variables is known as equation. Also, an equation in which the highest power of the variable is one with one or more variables, is known as linear equation. For example, the algebraic equation ax + b = 0 is a linear equation in one variable. Similarly, the algebraic equation ax + by + c = 0, is a linear equation in two variables.
The given equation in the question is:
$10x – 9y = 12 …. (1)$
Now, we have its solution pair as:
(2k – 1, k).
Therefore, we have
$x = 2k-1$
And $y = k$.
Now we substitute above values in equation (1) , then we get
$10\times (2k -1) - 9\times k = 12…….(2)$
This is a linear equation in a single variable k .
Now, we will simplify the equation (2) as follows,
$20 k -10 – 9k = 12$
$ \Rightarrow 11k = 12 + 10$
$ \Rightarrow 11 \times k = 22$
$ \Rightarrow k = 2$
$\therefore $ The value of K will be $2$.

So, the correct answer is “Option B”.

Note:This problem is a simple one taken from the linear equations in two variables. Simple algebraic substitution and further simplification will solve such equations with required result.