Question

If the pair of linear Equation" x + 2y = 3and 2x+4y =k
coincide then the value of 'k' is​

Answer 1

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Given:

• Equations, x + 2y = 3 & 2x + 4y = k

To Find:

• Value of k, such that the equations coincide.

Concept:

We know that, a pair of linear equations can have 3 cases.

1. They will intersect at some point.
2. They will never intersect, i.e., they are parallel.
3. They lie on each other,i.e., they coincide.

For each case, there is a different scenario.

Let there be 2 linear equations, $a_1x+b_1y=c_1$ and $a_2x+b_2y=c_2$.

For 1st case, i.e., when they intersect at a point,

• $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$

For 2nd case, i.e., when they are parallel,

• $\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$

For 3rd case, i.e., when they coincide,

• $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$

Solution:

Here,

$a_1 = 1, b_1 = 2, c_1 = 3, a_2 = 2, b_2 = 4, c_2 = k$

So, as the question gives us the 3rd case, we compare the ratios so as to find the value of k.

$:\implies \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2} \\\\:\implies \dfrac{1}{2} = \dfrac{2}{4} = \dfrac{3}{k} \\\\:\implies k = 3*2 \\\\\bf{:\implies k = 6}$

Hope it helps!!!

Answer 2

Answer:

by elimination method Is easy to do brother