Question 1 :
2x + 3y = 5
x - 3y = -2
Question 2 :
3x - 2y = 1
5x - 3y = 3
Question 3 :
1/2x + 1/3y = 2
1/3x + 1/2y = 13/6
Question 4 :
2/√x + 3/√y = 2
4/√x – 9/√y = -1
Question 5 :
4/x + 3y = 14
3/x – 4y = 23
1. Answer :
2x + 3y = 5 ----(1)
x - 3y = -2 ----(2)
(1) + (2) :
3x = 3
Divide both sides by 3.
x = 1
Substitute x = 1 in (1).
2(1) + 3y = 5
2 + 3y = 5
Subtract 2 from both sides.
3y = 3
Divide both sides by 3.
y = 1.
Therefore,
x = 1 and y = 1
2. Answer :
3x - 2y = 1 ----(1)
5x - 3y = 3 ----(2)
In the above equation, none of the variables have the same coefficient in both the equations.
Let's eliminate the variable y. Consider the coefficients of y in the above two equations. The coefficients of y are 2 and 3 (without considering the sign).
Least common multiple of (2, 3) = 6.
Make the coefficient of y as 6 in both the equations multiplying by suitable factors.
And also, when you multiply, make sure that the y-terms have different signs in the two equations. So that, when you add the equations, y-terms can be eliminated.
3x(1):
9x - 6y = 3 ----(3)
-2x(2):
-10x + 6y = -6 ----(4)
(3) + (4) :
-x = -3
Multiply both sides by -1.
x = 3.
Substitute x = 3 in (1).
3(3) - 2y = 1
9 - 2y = 1
Subtract 9 from both sides.
-2y = -8
Divide both sides by -2.
y = 4.
Therefore,
x = 3 and y = 4
3. Answer :
1/2x + 1/3y = 2
1/3x + 1/2y = 13/6
Let a = 1/x and b = 1/y.
1/2x + 1/3y = 2 :
a/2 + b/3 = 2
Multiply both sides by 6.
6(a/2 + b/3) = 6(2)
6(a/2) + 6(b/2) = 12
3a + 2b = 12 ----(1)
1/3x + 1/2y = 13/6 :
a/3 + b/2 = 13/6
Multiply both sides by 6.
6(a/3 + b/2) = 6(13/6)
6(a/3) + 6(b/2) = 13
2a + 3b = 13 ----(2)
3x(1) :
9a + 6b = 36 ----(3)
-2x(2) :
-4a - 6b = -26 ----(4)
(3) + (4) :
5a = 10
Divide both sides by 5.
a = 2
Substitute a = 2 in (1).
3(2) + 2b = 12
6 + 2b = 12
Subtract 6 from both sides.
2b = 6
Divide both sides by 2.
b = 3
Solve for x and y :
1/x = a 1/x = 2 x = 1/2 |
1/y = b 1/y = 3 y = 1/3 |
4. Answer :
2/√x + 3/√y = 2
4/√x – 9/√y = -1
Let a = 1/√x and b = 1/√y.
2/√x + 3/√y = 2 :
2a + 3b = 2 ----(1)
4/√x – 9/√y = -1 :
4a – 9b = -1 ----(2)
3x(1) :
6a + 9b = 6 ----(3)
(2) + (3) :
10a = 5
Divide both sides by 10.
a = 1/2
2(1/2) + 3b = 2
1 + 3b = 2
Subtract 1 from both sides.
3b = 1
Divide both sides by 3.
b = 1/3
Solve for x and y :
1/√x = 1/2 √x = 2 x = 22 x = 4 |
1/√y = 1/3 √y = 3 y = 32 y = 9 |
5. Answer :
4/x + 3y = 14
3/x – 4y = 23
Let a = 1/x and b = y.
4/x + 3y = 14 :
4a + 3b = 14 ----(1)
3/x – 4y = 23 :
3a – 4b = 23 ----(2)
4x(1) :
16a + 12b = 56 ----(3)
3x(2) :
9a – 12b = 69 ----(4)
(3) + (4) :
25a = 125
Divide both sides by 25.
a = 5
Substitute a = 5 in (1).
4(5) + 3b = 14
20 + 3b = 14
Subtract 20 from both sides.
3b = -6
Divide both sides by 3.
b = -2
1/x = a 1/x = 5 x = 1/5 |
y = b y = -2 |
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