3x/2-5y/3=-2, x/3+y/2=13/6 solve equations in substitution method

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 1. Solve the following pair of linear equations by the substitution method.

(vi) 3x/2-5y/3=-2, x/3+y/2=13/6

Solution

(3x)/2-(5y)/3=2

Make lcm of 2/3

(9x-10y)/6=-2

9x-10y=-12

x/3+y/2=13/6

make lcm of 3,2

(2x+3y)/6=13/6

2x+3y=6x13/6

2x+3y=13--------(2)

Let we take equation (1) and make x form

9x-10y=-12

9x=10y-12

X=(10y=12)/3--------(3)

Substitute x value in equation (2)

2x+3y=13

2(10y-12)/9+3y=13

(20y-24)/9+3y=13

(20y-24+27y)/9+3y=13

47y-24=117

47y=117+24=141

Y=141/47=3

Substitute y value in equation (3)

X=(10y-12)/9=10(3)-12/9=30-12=9=18/9=2

X=2, Y=3

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