Question

The pair of linear equations which has unique solution as x=3 and y= -1 is
class 10th​

Answer 1

Answer:

If x = 2, y = -3 is a unique solution of any pair of equation, then these values must satisfy that pair of equations.

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A pair of linear equations which has a unique solution x = 2 and y = -3 is.

Answer 2

Linear Equation

Given:

x=3 and y=-1

To find:

Pair of linear equations which has unique solution as x=3 and y= -1

Explanation:

$a_{1}\times3+b_{1}\times(-1)+c_1=0\\a_{1}x+b_{1}y+c_1=0\\a_{2}x+b_{2}y+c_2=0$

The lines has unique solution x=3 and y=-1 so it should satisfy the above equations

$a_{1}\times3+b_{1}\times(-1)+c_1=0$

AND

$a_{2}\times3+b_{2}\times(-1)+c_2=0\\\implies3a_1-b_1+c_1=0---------------(i)\\\implies3a_2-b_2+c_2=0---------------(ii)$

the restricted values of $a_1, a_2, b_1 and\ b_2$  is

$\frac{a_1}{a_2} =\frac{b_1}{b_2}-----------------(iii)$

Hence all the real values of will satisfy the equation (i) and (ii) having solutions as , only things limits the values is which satisfies equation (iii).

So, infinite number of solutions can be possible for the system of equations which has unique solutions as x=3 and y=-1. Infinite number of lines can intersect through point (3,-1).