X+y=a-b,ax-by=a2+b2 by cross multiplication
Answers
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:
x + y= a + b , ax – by= a² - b².
The given system of equations may be written as:
x + y-( a + b)= 0 , ax – by -( a² - b²)= 0.
a1= 1, b1= 1, c1= -(a+b)
a2= a , b2= -b , c2= -(a²-b²)
x y 1
----------- = ----------------- = ---------
b1 c1 c1 a1 a1 b1
b2 c2 c2 a2 a2 b2
x y 1
----------------- ------------- = ---------
1 - a-b -a-b 1 1 1
-b -a²+b² -a²+b² a a -b
x y
---------------------- = ----------------------- =
-(a²-b²)-(-b)×-(a+b) (-a-b)×a -(-a²+b²)×1
1
-----------
1×-b -a×1
x y 1
----------- = --------------- = -----------------
(-a²+b²)-ab-b² -a²-ab+a²-b² -b -a
x y 1
--------- = -------- = ----------
-a²-ab -ab - b² -a - b
x y 1
--------- = -------- = ----------
-a(a+b) -b(a + b) -(a + b)
x= -a(a+b) /-(a + b)
x= a
y = -b(a + b) / -(a + b)
y= b
Hence , the solution of the given system of equation is x= a , y= b
HOPE THIS WILL HELP YOU..
Answer:
here you can use The actual procedure of Cross-Multiplication
or Cross-Multiplication formula
for detailed solution plz refer above image
Ans: x = a, y = b
