Question

for what value of k the equation 2x-3y+10=0 and 3x+ky+15=0 represent coincident line​

Answer 1

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Answer 2

Given:

Two equations 2x-3y+10=0 and 3x+ky+15=0.

To find:

The value of k for which given equations represent the coincident line.

Solution:

Two linear equations ax + by + c = 0 and lx + my + n = 0 having two variables x and y are said to form a coincident line on the graph if

$\frac{a}{l} = \frac{b}{m} = \frac{c}{n}$

Therefore, the given equations 2x-3y+10=0 and 3x+ky+15=0 represent a coincident line if

$\frac{2}{3} = \frac{ - 3}{k} = \frac{10}{15}$

$\frac{2}{3} = \frac{ - 3}{k} \: and \: \frac{ - 3}{k} = \frac{10}{15}$

$2k = - 9$

$k = \frac{ - 9}{2}$

Hence, the value of k for which given equations 2x-3y+10=0 and 3x+ky+15=0 represent a coincident line is -9/2.