Question

If the pair of equations 2x + 3y = 5 and 5x + (15/2) y = k represent two coincident lines, then the value of k is​

Answer 1

Given that,

The pair of equations $2x+3y=5$ and $5x+\dfrac{15}{2}y=k$ represent two coincident lines.

To find,

The value of k.

Solution,

For two coincident lines, $\dfrac{a_1}{a_2} =\dfrac{b_1}{b_2} =\dfrac{c_1}{c_2}$ here a,b and c are coefficients of lines. We have,

$a_1=2,a_2=5\\\\b_1=3, b_2=\dfrac{15}{2}\\\\c_1=5,c_2=k$

So,

$\dfrac{2}{5} =\dfrac{3}{7.5} =\dfrac{5}{k}$

$\dfrac{2}{5}=\dfrac{5}{k}, \dfrac{3}{7.5}=\dfrac{5}{k}\\\\k=5, k = 12.5$

So, the value of k can be 5 or 12.5 so that the two lines are coincident.

Learn more,

Coincident lines

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Answer 2

Answer:

Step-by-step explanation: