Question

Solve by the substitution method :-

$\frac{3x}{2} - \frac{5y}{3} = - 2 \\ \frac{x}{3} + \frac{y}{2} = \frac{13}{6}$



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Answer 1

3x/2 - 5y/3 = -2 ⠀⠀⠀⠀ x/3 + y/2 = 13/6

9x - 10y/6 = -2 ⠀⠀⠀⠀2x + 3y/6 = 13/6

9x - 10y = -12 _(i) ⠀⠀ 2x + 3y = 13 _(ii)

• Multiply the equation (i) by 3 & (ii) by 10

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

27x - 30y = -36⠀⠀⠀⠀20x + 30y = 130

• Add both

27x - 30y + 20x + 30y = -36 + 130

27x + 20x = -94

47x = -94

x = -2

• Put x = -2 in (ii)

2x + 3y = 13

2(-2) + 3y = 13

-4 + 3y = 13

3y = 13 - 4

3y = 9

y = 9/3

y = 3

Answer 2

Step-by-step explanation:

3x/2 - 5y/3 = -2 ⠀⠀⠀⠀ x/3 + y/2 = 13/6

9x - 10y/6 = -2 ⠀⠀⠀⠀2x + 3y/6 = 13/6

9x - 10y = -12 _(i) ⠀⠀ 2x + 3y = 13 _(ii)

Multiply the equation (i) by 3 & (ii) by 10

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

27x - 30y = -36⠀⠀⠀⠀20x + 30y = 130

Add both

27x - 30y + 20x + 30y = -36 + 130

27x + 20x = -94

47x = -94

x = -2

Put x = -2 in (ii)

2x + 3y = 13

2(-2) + 3y = 13

-4 + 3y = 13

3y = 13 - 4

3y = 9

y = 9/3

y = 3

hope it helps you