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Ncert exemplar solutions

CHAPTERS

**–** *x***+** *py***= 1 and** *px***–** *y***= 1, if the pair of equations has no solution. Find p.**

Given pair of linear equations is

– x + py = 1 …(i)

px – y – 1 = 0 …(ii)

On comparing with ax + by + c = 0,

We get,

a_{1} = -1, b_{1} = p, c_{1} =- 1;

a_{2} = p, b_{2} = – 1, c_{2} =- 1;

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

b_{1} /b_{2} = – p

c_{1} /c_{2} = 1

Since, the lines equations has no solution i.e., both lines are parallel to each other.

a_{1}/a_{2} = b_{1}/b_{2}≠ c_{1}/c_{2}

-1/p = – p ≠ 1

Taking last two parts, we get

p ≠ -1

Taking first two parts, we get

p^{2} = 1

p = + 1

Hence, the given pair of linear equations has no solution for p = 1.

**–** *x***+** *py***= 1 and** *px***–** *y***= 1, if the pair of equations has no solution. Find p.**

Given pair of linear equations is

– x + py = 1 …(i)

px – y – 1 = 0 …(ii)

On comparing with ax + by + c = 0,

We get,

a_{1} = -1, b_{1} = p, c_{1} =- 1;

a_{2} = p, b_{2} = – 1, c_{2} =- 1;

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

b_{1} /b_{2} = – p

c_{1} /c_{2} = 1

Since, the lines equations has no solution i.e., both lines are parallel to each other.

a_{1}/a_{2} = b_{1}/b_{2}≠ c_{1}/c_{2}

-1/p = – p ≠ 1

Taking last two parts, we get

p ≠ -1

Taking first two parts, we get

p^{2} = 1

p = + 1

Hence, the given pair of linear equations has no solution for p = 1.

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