Question
Solve for x and y:
7(y + 3) - 2(x + 2) = 14,
4(y - 2) + 3(x - 3) = 2
7(y + 3) - 2(x + 2) = 14,
4(y - 2) + 3(x - 3) = 2
✓
Answer
The given equations are: 7(y + 3) - 2(x + 2) = 14 4(y - 2) + 3(x - 3) = 2 7(y + 3) - 2(x + 2) = 14⇒ 7y + 21 - 2x - 4 = 14
⇒ 7y - 2x = 14 + 4 - 21
⇒ -2x + 7y = -3 ...(1)
4(y - 2) + 3(x - 3) = 2⇒ 4y - 8 + 3x - 9 = 2
⇒ 4y + 3x = 2 + 8 + 9
⇒ 3x + 4y = 19 ...(2)
Multiply (1) by 4 and (2) by 7, we get
-8x + 28y = -12 ...(3)
21x + 28y = 133 ...(4)
Subtracting (3) and (4), we get
29x = 145
x = 5
Substituting x = 5 in (1), we get
-2 × 5 + 7y = -3
⇒ 7y = -3 + 10
⇒ 7y = 7
⇒ y = 1
$\therefore$ Solution is x = 5 and y = 1
⇒ 7y - 2x = 14 + 4 - 21
⇒ -2x + 7y = -3 ...(1)
4(y - 2) + 3(x - 3) = 2⇒ 4y - 8 + 3x - 9 = 2
⇒ 4y + 3x = 2 + 8 + 9
⇒ 3x + 4y = 19 ...(2)
Multiply (1) by 4 and (2) by 7, we get
-8x + 28y = -12 ...(3)
21x + 28y = 133 ...(4)
Subtracting (3) and (4), we get
29x = 145
x = 5
Substituting x = 5 in (1), we get
-2 × 5 + 7y = -3
⇒ 7y = -3 + 10
⇒ 7y = 7
⇒ y = 1
$\therefore$ Solution is x = 5 and y = 1
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