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Linear Equations in Two Variables
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08/07/2021 11:13 am
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Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?
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08/07/2021 11:17 am
Equation of 2 lines passing through (2, 14) should be in such a way that it satisfies the point.
Let the equation be, 7x = y
7x – y = 0
When x = 2 and y = 14
(7 × 2) - 14 = 0
14 – 14 = 0
0 = 0
L.H.S = R.H.S
Let another equation be, 4x = y-6
4x-y+6 = 0
When x = 2 and y = 14
(4 × 2 – 14 + 6 = 0
8 – 14 + 6 = 0
0 = 0
L.H.S = R.H.S
Since both the equations satisfies the point (2, 14), than say that the equations of two lines passing through (2, 14) are 7x = y and 4x = y - 6
We know that, infinite number of line passes through one specific point. Since there is only one point (2, 14) here, there can be infinite lines that passes through the point.