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Ncert exemplar solutions

CHAPTERS

**2 x**

Given, pair of linear equations is

2x + 3y – 5 = 0

px – 6y – 8 = 0

On comparing with ax + by + c = 0 we get

Here, a_{1} = 2, b_{1} = 3, c_{1} = – 5;

And a_{2} = p, b_{2} = – 6, c_{2} = – 8;

a_{1} /a_{2} = 2/p

b_{1} /b_{2} = – 3/6 = – ½

c_{1} /c_{2} = 5/8

Since, the pair of linear equations has a unique solution.

a_{1}/a_{2} ≠ b_{1}/b_{2}

so 2/p ≠ – ½

p ≠ – 4

Hence, the pair of linear equations has a unique solution for all values of p except – 4.

**2 x**

Given, pair of linear equations is

2x + 3y – 5 = 0

px – 6y – 8 = 0

On comparing with ax + by + c = 0 we get

Here, a_{1} = 2, b_{1} = 3, c_{1} = – 5;

And a_{2} = p, b_{2} = – 6, c_{2} = – 8;

a_{1} /a_{2} = 2/p

b_{1} /b_{2} = – 3/6 = – ½

c_{1} /c_{2} = 5/8

Since, the pair of linear equations has a unique solution.

a_{1}/a_{2} ≠ b_{1}/b_{2}

so 2/p ≠ – ½

p ≠ – 4

Hence, the pair of linear equations has a unique solution for all values of p except – 4.

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