Question

ax +by =c
a2x+b2y=c2​

Answer 1

Answer:

b²

Step-by-step explanation:

CROSS - MULTIPLICATION METHOD:

The general form of a pair of linear equations

a1x + b1y + c1 = 0 , &        a2x + b2y + c2 = 0.

When a1 / a2 ≠ b1 / b2, the pair of linear equations will have a unique solution.

To solve this pair of equations for x and y using cross-multiplication, we’ll arrange the variables x and y and their coefficients a1, a2, b1 and b2, and the constants c1 and c2  as shown below

⇒ x =  b1 c2 - b2 c1  / a1 b2 - a2 b1    

⇒ y =  c1 a2 - c2 a1  / a1 b2 - a2 b1

The above equation is generally written as :

x/ b1 c2 - b2 c1 =  y/ c1 a2 - c2 a1 = 1/a1 b2 - a2 b1

SOLUTION is in the attachment also.

x /a +y / b= a  +  b , x/ a² + y/b²= 2.

a1= 1/a, b1= 1/b, c1= -(a+b)= -a-b

a2= 1/a² , b2= 1/b² , c= -2

    x                       y                       1

-----------   =   -----------------     =    -------------

b1      c1        c1           a1           a1        b1

b2      c2       c2           a2           a2       b2

     x                          y                        1

-----------------   =    -------------------  =   ---------

1/b    - a-b           -a-b     1/a         1/a    1/b

1/b²   -2               -2       1/a²         1/a²  1/b²

   x                     y                            1

----------- =   ---------------  =    -----------------

-2/b +(a+b)/b²   -(a+b)/a² + 2/a   1/ab² -1/ba²

x b²         a² y               a² b²

---------   = --------  =     ----------

a - b        a - b              a - b

x = a²    and  y = b²      

Hence the value of x = a² & y = b²CROSS - MULTIPLICATION METHOD:

The general form of a pair of linear equations

a1x + b1y + c1 = 0 , &        a2x + b2y + c2 = 0.

When a1 / a2 ≠ b1 / b2, the pair of linear equations will have a unique solution.

To solve this pair of equations for x and y using cross-multiplication, we’ll arrange the variables x and y and their coefficients a1, a2, b1 and b2, and the constants c1 and c2  as shown below

⇒ x =  b1 c2 - b2 c1  / a1 b2 - a2 b1    

⇒ y =  c1 a2 - c2 a1  / a1 b2 - a2 b1

The above equation is generally written as :

x/ b1 c2 - b2 c1 =  y/ c1 a2 - c2 a1 = 1/a1 b2 - a2 b1

SOLUTION is in the attachment also.

x /a +y / b= a  +  b , x/ a² + y/b²= 2.

a1= 1/a, b1= 1/b, c1= -(a+b)= -a-b

a2= 1/a² , b2= 1/b² , c= -2

    x                       y                       1

-----------   =   -----------------     =    -------------

b1      c1        c1           a1           a1        b1

b2      c2       c2           a2           a2       b2

     x                          y                        1

-----------------   =    -------------------  =   ---------

1/b    - a-b           -a-b     1/a         1/a    1/b

1/b²   -2               -2       1/a²         1/a²  1/b²

   x                     y                            1

----------- =   ---------------  =    -----------------

-2/b +(a+b)/b²   -(a+b)/a² + 2/a   1/ab² -1/ba²

x b²         a² y               a² b²

---------   = --------  =     ----------

a - b        a - b              a - b

x = a²    and  y = b²      

Hence the value of x = a² & y = b²