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Bunuel
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IMO B

3x + 2y = 6 - multiplying by 3
4x - 3y = 4, multiplying by 2

9x + 6y = 18
8x - 6y = 8
Adding both equations
17x = 26
x = 26/17
putting value in equation 3x+2y=6
3*26/17-6 =-2y
78-102/17 = -2y
-24/17 = -2y
12/17 = y

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Explanation :
{3x + 2y = 6 }x3
{4x - 3y = 4 }x2
we get:
9x + 6y = 18---1
8x - 6y = 8---2
From 1 & 2,
17x = 26
x= 26/17
so, y = 12/17

IMO-B
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Bunuel
If 3x + 2y = 6 and 4x - 3y = 4, what is the value of y?

A. 12/19
B. 12/17
C. 12/13
D. 12/11
E. 17/12

Asked: If 3x + 2y = 6 and 4x - 3y = 4, what is the value of y?

(3x + 2y = 6)*4
12x + 8y = 24
(4x - 3y = 4)*3
12x - 9y = 12

17y = 12
y = 12/17

IMO B
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\(3x+2y=6\)
\(4(3x+2y)=4*6\)
\(12x+8y=24\)

\(4x-3y=4\)
\(3(4x-3y)=3*4\)
\(12x-9y=12\)

\((12x+8y)-(12x-9y)=24-12\)
\(17y=12\)
\(y=\frac{12}{17}\)
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Perfect workflow to find the solution but to get you there quicker - multiply the top equation by -4 and bottom equation by 3. This will enable you to cancel out the x variable and immediately solve for Y, saving you time as you don't need to replug back in.
yashikaaggarwal
3x + 2y = 6 multiply whole equation with 3
4x - 3y = 4, multiply whole equation with 2

9x + 6y = 18
8x - 6y = 8
equating both
17x = 26
x = 26/17
putting value in equation 3x+2y=6
3*26/17-6 =-2y
78-102/17 = -2y
-24/17 = -2y
12/17 = y

answer is B
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