How to solve linear equations by elimination method?
Step 1 :
By taking anyone equations from the given two equations ,first multiply by some suitable non-zero constant to make the co-efficient of one variable (either x or y) numerically equal.
Step 2 :
If both coefficients are numerically equal to the same sign, then we may eliminate them by subtracting those equations.
If they have different signs, then we may add both equations and eliminate them.
Step 3 :
After eliminating one variable, we may get the value of one variable.
Step 4 :
The remaining variable is then found by substituting in any one of the given equations.
Problem 1 :
3x + y = 7
-2x - y = 9
Solution :
3x + y = 7 ---> (1)
-2x - y = 9 ---> (2)
Add (1) + (2), we get
3x + y - 2x - y = 7 + 9
x = 16
By applying x = 16 in (1) equation, we get
3(16) + y = 7
48 + y = 7
y = 7 - 48
y = -41
Therefore, the solution is x = 16 and y = -41.
Problem 2 :
4x + 3y = 2
2x - 3y = 1
Solution :
4x + 3y = 2 ---> (1)
2x - 3y = 1 ---> (2)
Add (1) + (2), we get
4x + 3y + 2x - 3y = 2 + 1
6x = 3
x = 1/2
By applying x = 1/2 in (1) equation, we get
4(1/2) + 3y = 2
2 + 3y = 2
3y = 2 - 2
3y = 0
y = 0
Therefore, the solution is x = 1/2 and y = 0.
Problem 3 :
2x + 2y = 3
x = 4y - 1
Solution :
2x + 2y = 3 ---> (1)
x - 4y = -1 ---> (2)
(1) ∙ 2 ==> 4x + 4y = 6 ----> (3)
Add (3) + (2), we get
4x + 4y + x - 4y = 6 - 1
5x = 5
x = 1
By applying x = 1 in (1) equation, we get
2(1) + 2y = 3
2 + 2y = 3
2y = 3 - 2
2y = 1
y = 1/2
Therefore, the solution is x = 1 and y = 1/2.
Problem 4 :
y = 1 + x
2x + y = -2
Solution :
y = 1 + x
x - y = -1 ---> (1)
2x + y = -2 ---> (2)
Add (1) + (2), we get
x - y + 2x + y = -1 - 2
3x = -3
x = -1
By applying x = -1 in equation (1)
y = 1 - 1
y = 0
Therefore, the solution is x = -1 and y = 0.
Problem 5 :
1/2x + 4y = 4
2x - y = 1
Solution :
1/2x + 4y = 4 ---> (1)
2x - y = 1 ---> (2)
(1) ∙ 4 ==> 8x - 4y = 4 ---> (3)
Add (1) + (3), we get
1/2x + 4y + 8x - 4y = 4 + 4
17/2x = 8
17x = 16
x = 16/17
By applying x = 16/17 in equation (2)
2(16/17) - y = 1
32/17 - y = 1
-y = (17 - 32) / 17
-y = -15/17
y = 15/17
Therefore, the solution is x = 16/17 and y = 15/17.
Problem 6 :
y = x - 4
4x + y = 26
Solution :
y = x - 4
x - y = 4 ---> (1)
4x + y = 26 ---> (2)
Add (1) + (2), we get
x - y + 4x + y = 4 + 26
5x = 30
x = 6
By applying x = 6 in equation (1)
y = 6 - 4
y = 2
Therefore, the solution is x = 6 and y = 2.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM