Q51 of 59 Page 178

State whether the statements are true or false.

The straight line 5x + 4y = 0 passes through the point of intersection of the straight lines x + 2y – 10 = 0 and 2x + y + 5 = 0.

Given equation are

x + 2y – 10 = 0 …(i)


and 2x + y + 5 = 0 …(ii)


Firstly, we find the point of intersection:


Multiplying the eq. (i) by 2, we get


2x + 4y – 20 = 0 …(iii)


On subtracting eq. (iii) from (ii), we get


2x + y + 5 – 2x – 4y + 20 = 0


⇒ -3y + 25 = 0


⇒ -3y = -25



Putting the value of y in eq. (i), we get




⇒ 3x + 20 = 0




If the given line 5x + 4y = 0 passes through the point then




⇒ 0 = 0


So, the given line passes through the point of intersection of the given lines.


Hence, the given statement is TRUE


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