Question

write the pair of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0 such that a1=2,b1=3,a2=5,b2=-1 and has a unique solution,x=-1,y=3.how many such pairs can be written using different values of a1,b1,a2,b2​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given that,

$a_{1}=2$

$b_{1}=3$

$a_{2}=5$

$b_{2}=-1$

$x=-1$

$y=3$

The pair of line equations

$a_{1}x+b_{1}y+c_{1}=0$...(I)

$a_{2}x+b_{2}y+c_{2}=0$....(II)

We need to to calculate the value of c₁

Using equation (I)

$a_{1}x+b_{1}y+c_{1}=0$

Put the value of a,b, x and y

$2\times-1+3\times3+c_{1}=0$

$c_{1}=-7$

We need to to calculate the value of c₂

Using equation (II)

$a_{2}x+b_{2}y+c_{2}=0$

Put the value of a,b, x and y

$5\times-1-1\times3+c_{1}=0$

$c_{1}=9$

Now, We need to find the pair of $\dfrac{a_{1}}{a_{2}}$, $\dfrac{b_{1}}{b_{2}}$ and $\dfrac{c_{1}}{c_{2}}$

Put the value in the pair

$\dfrac{a_{1}}{a_{2}}=\dfrac{2}{5}$

$\dfrac{b_{1}}{b_{2}}=\dfrac{3}{-1}$

$\dfrac{c_{1}}{c_{2}}=\dfrac{-7}{9}$

So, $\dfrac{2}{5}\neq\dfrac{2}{-1}\neq\dfrac{-7}{9}$

We can say that more pairs for different values of a₁,a₂,b₁ and b₂.

Hence, These equations have unique solution.