Question

The pair of equations ax + 5y = 12 and 2x - by = 15 represents the parallel lines, then the value of ab
equals​

Answer 1

Answer:

$ab=-10$

Step-by-step explanation:

Given parallel lines: ax+5y=12 and 2x-by=15

We can write them as:

$y=-\dfrac{a}{5}x+\dfrac{12}{5} \; \: and \; \: y= \dfrac{2}{b}x -\dfrac{15}{b}$

The slope of parallel lines remain same. Therefore,

$\dfrac{-a}{5} = \dfrac{2}{b} \\\\\rightarrow ab=-10$

Answer 2

Given : The equations given are ax + 5y = 12 & 2x - by = 15.

• They both represents the parallel lines.

Find: The value of ab .

Solution:

• Two lines are said to be parallel if their slopes are same.

• But they have different y intercepts.

• Here , the slope means a measure of its steepness i.e dy/dx.

• As we know that they are parallel lines and they have same slope ,so for finding the value of ab we can write the pair of equations like this in the terms of y.

• y = - ax/5 + 12/5 & y = 2x/b - 15/b

• As slope of the parallel lines remain same so we can write it like this :

=> -a/2 = 5/b

=> ab = -10.

• So , the value of ab is -10.