Question

a2x+b2y=c2,b2x+a2y=d2​

Answer 1

Answer:

The soluition is

$x=\frac{b_2c_1-b_1c_2}{a_1b_2-a_2b_1}$

$y=\frac{a_1c_2-a_2c_1}{a_1b_2-a_2b_1}$

Step-by-step explanation:

I have solved the given system of linear equations by cross multiplication method.

Given equations are

$a_1x+b_1y=c_1$

$a_2x+b_2y=c_2$

$a_1x+b_1y-c_1=0$

$a_2x+b_2y-c_2=0$

By cross multiplication rule,

$\frac{x}{-b_1c_2+b_2c_1}=\frac{y}{-a_2c_1+a_1c_2}=\frac{1}{a_1b_2-a_2b_1}$

$\frac{x}{b_2c_1-b_1c_2}=\frac{y}{a_1c_2-a_2c_1}=\frac{1}{a_1b_2-a_2b_1}$

Now,

$\frac{x}{b_2c_1-b_1c_2}=\frac{1}{a_1b_2-a_2b_1}$

$x=\frac{b_2c_1-b_1c_2}{a_1b_2-a_2b_1}$

and

$\frac{y}{a_1c_2-a_2c_1}=\frac{1}{a_1b_2-a_2b_1}$

$y=\frac{a_1c_2-a_2c_1}{a_1b_2-a_2b_1}$

The soluition is

$x=\frac{b_2c_1-b_1c_2}{a_1b_2-a_2b_1}$

$y=\frac{a_1c_2-a_2c_1}{a_1b_2-a_2b_1}$

Answer 2

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