Engineering
Mathematics
Introduction to Determinants
Question

The straight lines x + 2y – 9 = 0, 3x + 5y – 5 = 0 and ax + by – 1 = 0 are concurrent if the straight line 22x – 35y – 1 = 0 passes through the point

(a, b)

(b, a)

(– a, b)

(– a, – b)

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Solution
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x + 2y – 9 = 0            ---(1)

3x + 5y – 5 = 0         ---(2)

ax + by – 1 = 0         ---(3)

Solving (1) and (2) simultaneously we get 

y = 22, x = – 35

Now, equation (1), (2) and (3) will be concurrent, that is they will pass through one point if y = 22, x = – 35 satisfy the third equation ax + by – 1 = 0.

Substituting the values of 'x' and 'y' in this equation we get – 35a + 22b – 1 = 0    ---(4)

And another equation given is 22x – 35y – 1 = 0        ---(5)

Equation (5) will be of the form of equation (4), if we substitute

x = b & y = a

That is 22x – 35y – 1 = 0 passes through (b, a)

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