Question
Solve for x and y:
6x + 5y = 7x + 3y + 1 = 2(x + 6y - 1)
6x + 5y = 7x + 3y + 1 = 2(x + 6y - 1)
✓
Answer
The given equations are: 6x + 5y = 7x + 3y + 1 = 2(x + 6y - 1) Therefore, we have 6x + 5y = 2(x + 6y - 1)⇒ 6x + 5y = 2x + 12y - 2
⇒ 6x - 2x + 5y - 12y = -2
4x - 7y = -2 ...(1) 7x + 3y + 1 = 2(x + 6y - 1)⇒ 7x + 3y + 1 = 2x + 12y - 2
⇒ 7x - 2x + 13y - 12y = -2 - 1
5x - 9y = -3 ...(2)Multiply (1) by 9 and (2) by 7, we get
36x - 63y = -18 ...(3)
35x - 63y = -21 ...(4)
Subtracting (4) from (3), we get
x = 3
Substituting x = 3 in (1), we get
4 × 3 - 7y = -2
⇒ -7y = -2 - 12
⇒ -7y = -14
⇒ y = 2
$\therefore$ Solution is x = 3 and y = 2
⇒ 6x - 2x + 5y - 12y = -2
4x - 7y = -2 ...(1) 7x + 3y + 1 = 2(x + 6y - 1)⇒ 7x + 3y + 1 = 2x + 12y - 2
⇒ 7x - 2x + 13y - 12y = -2 - 1
5x - 9y = -3 ...(2)Multiply (1) by 9 and (2) by 7, we get
36x - 63y = -18 ...(3)
35x - 63y = -21 ...(4)
Subtracting (4) from (3), we get
x = 3
Substituting x = 3 in (1), we get
4 × 3 - 7y = -2
⇒ -7y = -2 - 12
⇒ -7y = -14
⇒ y = 2
$\therefore$ Solution is x = 3 and y = 2
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