find value of x and y
99x + 101y = 499
101x + 99y = 501
Answers
Given
99x + 101y = 499
101x + 99y = 501
On sbstracting both equation we get
x(99 - 101) + y(102- 99)= 2
(X + y) = 1
on multiplying both side by 99
99x +99y = 99
on subtracting in equation 1 of equation 3 we get
2y = 400
y = 200
so
x = -199
#BAL
The line equation is in the form of
Ax + By = C
Bx + Ay = D
This is the shortcut route, u just have to remember the end answer
After solving this linear equation we get the value of x and y as
x = (AC - BD) / A^2 - B^2 And y = (AD - BC )/ A^2 - B^2
Here the value of A - 99 , B - 101 , C - 499 and D - 501
So the value of x = (99 * 499 - 101 *501) / (99^2 - 101^2) and
y = (99 * 501 - 101*499) /(99^2 - 101^2)
Thus solving the above equation gives value of x and y as
x = 3 and y = 2
OR u can solve both equation as
99 X + 101 Y = 499 ——-eq 1
101 X + 99 Y = 501 ———eq 2
solving both equations,
multiply eq 1 by 101 and eq 2 by 99
99 * 101 X + 101 * 101 Y = 499 *101
101 * 99 X + 99 * 99 Y = 501 * 99
999 X + 10201 Y = 50399 —- eq 3
999 X + 9801 Y = 49599 ——- eq4
Solving the above obtained equation for the value of X by subtracting eq 3 from eq 4
(10201 - 9801) Y = 50399 - 49599
Y = 800/400 = 2
Putting the value of Y = 2 in eq 1
99X + 101 * 2 =499
X = (499 - 202) / 99
X = 3
Answer for the equation for the value of x & Y are
X - 3 & Y- 2