Question

3x/2-5y/3=-2 and x/3+y/2=13/6 substitution method​

Answer 1

Answer:

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

multiplying throughout by 6

9x-10y=-12 (1)

x/3+y/2=13/6

multiplying throughout by 6

2x+3y=13

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

substituting eq 2 in 1

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

117-27y-20y=-24

-47y=-24-117

-47y=-141

y=3

substituting y=3 in eq 2

x=(13-3×3)/2

x=(13-9)/2

x=4/2

x=2

(2,3) is the solution of the given equation

Answer 2

Answer:

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Step-by-step explanation:

Given,

3x/2 - 5y/3 = -2 ⇒ eq. 1

x/3 + y/2 = 13/6 ⇒eq. 2

Finding the value of 'x' from eq. 2

x/3 + y/2 = 13/6

x/3 = 13/6 - y/2

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

x = 13/2 - 3y/2

Substituting the value of ' x ' in eq. 1

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

3( 13/2 - 3y/2 ) - 5y/3 = -2

13/2 - 3y/2 - 5y/3 = -2/3

- 3y/2 - 5y/3 = -2/3 - 13/2

-6y/6 - 10y/6 = -4/6 - 39/6

-16y/6 = - 43/6

-16y = [ -43 / 6 ] × 6

-16y = -43

- y = -43/16

 y = 43/6

Now finding the exact value of ' x '

x = 13/2 - 3y/2

x = 13/2 - ( 3 × 43 /16)/2

x = 13/2 - 129 / 8

x = 42 - 129 / 8

x = -87 / 8

∴ x = -87 / 8 & y = -43 / 6