Solve the following systems of equations by using cross multiplication method x/a+y/b=a+b;x/a2+y/b2=2.
Answers
Solve by Cross Multiplication method :x /a +y / b= a + b , x/ a² + y/b²= 2.
nikitasingh79
nikitasingh79
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 = b²