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Question
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.
Options
True
False
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Solution
This statement is True.
Explanation:
Given equations are x + 2y – 10 = 0 ......(i)
And 2x + y + 5 = 0 ......(ii)
From equation (i) x = 10 – 2y
Putting the value of x in equation (ii) we get
2(10 – 2y) + y + 5 = 0
⇒ 20 – 4y + y + 5 = 0
⇒ – 3y + 25 = 0
⇒ y = `25/3`
Putting the value of y in equation (iii) we get
x = `10 - 2(25/3)`
= `(30 - 50)/3`
= `(-20)/3`
∴ Point = `((-20)/3, 25/3)`
If the given line 5x + 4y = 0 passes through the point `((-20)/3, 25/3)`
`5((-20)/3) + 4(25/3)` = 0
⇒ `(-100)/3 + 100/3` = 0
⇒ 0 = 0 satisfied.
So, the given line passes through the point of intersection of the given lines.
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