Linear Equation with Rational co-efficients

Topic : Linear Equations

Question : Solve the system of linear equations.
(2/3) x + (4/5) y = 8
(5/4) x - (3/2) y = - 6

Solution :
(2/3) x + (4/5) y = 8 ------------- (1)
(5/4) x - (3/2) y = - 6 ------------- (2)

To eliminate fractions let us multiply whole equation (1) by 15 and equation (2) by 8
15 *(2/3) x + 15*(4/5) y = 15*8
10x +12y = 120
dividing by 2
5x+6y=60

8*(5/4) x - 8*(3/2) y = - 6*8
10x-12y=-48
divide by 2
5x-6y= -24

So the two equations are
5x+6y=60
5x-6y= -24

adding both the equations
10x = 36
x = 36/10
x=3.6
substituting the value of x in first equation
5x+6y=60
5(3.6)+6y=60
18.0+6y=60
6y=-18.0+60
6y= 42
y = 42/6
y=7