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NCERT Exemplar Solutions Class 10 Mathematics Solutions for Pair of Linear Equations in Two Variables - Exercise 3.3 in Chapter 3 - Pair of Linear Equations in Two Variables
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– 3x + 5y = 7 and 2px – 3y = 1, if the lines represented by these equations are intersecting at a unique point. Find p.
Answer:
Given, pair of linear equations is
– 3x + 5y = 7
2px – 3y = 1
On comparing with ax + by + c = 0, we get
Here, a1 = -3, b1 = 5, c1 = – 7;
And a2 = 2p, b2 = – 3, c2 = – 1;
a1 /a2 = -3/ 2p
b1 /b2 = – 5/3
c1 /c2 = 7
Since, the lines are intersecting at a unique point i.e., it has a unique solution
a1/a2 ≠ b1/b2
-3/2p ≠ -5/3
p ≠ 9/10
Hence, the lines represented by these equations are intersecting at a unique point for all real values of p except 9/10
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