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Question
Find the equation of the straight line passing through origin and the point of intersection of the lines x + 2y = 7 and x – y = 4.
Solution
The given equations are:
x + 2y = 7 ...(1)
x − y = 4 ...(2)
Subtracting (2) from (1), we get,
3y = 3
y = 1
From (2),
x = 4 + y
= 4 + 1
= 5
The required line passes through (0, 0) and (5, 1).
Slope of the line = `(1 - 0)/(5 - 0) = 1/5`
Required equation of the line is given by:
y – y1 = m(x – x1)
`=> y - 0 = 1/5(x - 0)`
`=>` 5y = x
`=>` x – 5y = 0
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