Question

solve the following.
following: 2x + 3y = 12 ; 5 x-3y=9​

Answer 1

2x + 3y = 12 =≥ Equation 1

5x - 3y = 9 =≥ Equation 2

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2x + 3y = 12

2x = 12 - 3y

$x = \dfrac{12 - 3y}{2}$

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substituting the value in equation 2,

5x - 3y = 9

$5( \frac{12 - 3y}{2} ) - 3y = 9$

By multiplying 5 with (12-3y/2)

$(\frac{60 - 15y}{2}) - 3y = 9$

LCM = 2

$\frac{(60 - 15y) - (2 \times 3y)}{2} = 9$

$\frac{60 - 15y - 6y}{2} = 9$

$\frac{60 - 21y}{2} = 9$

by transposing 2 to the RHS (Right Hand side)

$60 - 21y = 2 \times 9$

$60 - 21y = 18$

by transposing (-21y) to the RHS (Right Hand Side)

$60 = 18 + 21y$

Transposing 18 to the LHS (Left Hand Side)

$60 - 18 = 21y$

$42 = 21y$

$42 = 21 \times y$

Transposing 21 to the LHS (Left Hand Side)

$\frac{42}{21} = y$

$2 = y$

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y = 2

$x = \frac{12 - (3 \times 2)}{2}$

$x = \frac{12 - 6}{2}$

$x = \frac{6}{2}$

$x = 3$

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Verification:

substituting x for 3 and y for 2,

2x + 3y = 12

(2×3) + (3×2) = 12

6 + 6 = 12

LHS = RHS = 12

5x - 3y = 9

(5×3) - (3×2) = 9

15 - 6 = 9

LHS = RHS = 9

Hence verified

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Answer 2

Answer:

Hey

,Mate I just want u to refer the attachment provided below. It's crystal clear. Hope u understand. ✌ Peace.

I had answered this question in substitution method, u can try other methods to find out tha answer as like elimnation Or cross multiplication methods.

Let's verify the question, whether the value of X and y are unique or not.

x =3 and y = 2

Equation :- 2x + 3y =12

=>2(3)+3(2)=12

=>6+6=12

=>12=R.H.S

5x - 3y = 9

=>5(3)+3(2)=9

=>15-6=9

=>9=R.H.S

Hence, Proved