Under Elimination Method follow the below steps
Step 1: Multiply the given equations in a way that coefficient of given variables become equal.
Step 2: Eliminate the variable with equal coefficients and find solution.
Lets understand this method with the help following examples:
Example 1: Solve the following pair of examples:
3x + 2y = 25
7x + 3y = 50
Solution: Label the given equations as shown below:
3x + 2y = 25 ... (equation 1)
7x + 3y = 50 ... (equation 2)
Step 1: Multiply the given equations in a way that coefficient of given varaiables become equal.
Here, we multiply (equation 1) with 3 and (equation 2) with 2 which will make coefficients of y equal in both the given equations and we get:
9x + 6y = 75 ... (equation 3)
14x + 6y = 100 ... (equation 4)
Step 2: Eliminate the variable with equal coefficients and find solution.
Here, coefficients of y are equal, subtract (equation 3) from (equation 4) in order to eliminate y, as shown below:
(9x + 6y) - (14x + 6y) = 75 - 100
open brackets and we get:
9x + 6y - 14x - 6y = 75 - 100
solve like terms and we get:
-5x = -25
divide both sides by (-5) and we get:
x = 5
Now, put the value of x in either of the given equation. Here, we put value of x in (equation 1) and we get:
3 X 5 + 2y = 25
15 + 2y = 25
subtract 15 from both sides and we get:
2y = 10
Divide both sides by 2 and we get:
y = 5
Hence, the solution is x = 5 and y = 5
Example 2: Solve the following pair of examples:
-5x + 2y = -1
4x - 3y = -9
Solution: Label the given equations as shown below:
-5x + 2y = -1 ... (equation 1)
4x - 3y = -9 ... (equation 2)
Step 1: Multiply the given equations in a way that coefficient of given variables become equal.
Here, we multiply (equation 1) with 4 and (equation 2) with 5 which will make coefficients of x equal in both the given equations and we get:
-20x + 8y = -4 ... (equation 3)
20x - 15y = -45 ... (equation 4)
Step 2: Eliminate the variable with equal coefficients and find solution.
Here, coefficients of y are equal, so add both the equations as shown below:
(-20x + 8y) + (20x - 15y) = -4 + (-45)
open brackets and we get:
-20x + 8y + 20x - 15y = -4 - 45
solve like terms and we get:
-7y = -49
divide both sides by (-7) and we get:
y = 7
Now, put the value of y in either of the given equation. Here, we put value of y in (equation 2) and we get:
4x - 3 X 7= -9
4x - 21 = -9
4x = -9 + 21
4x = 12
Divide from both sides by 4 and we get:
x = 3
Hence, the solution is x = 3 and y = 7
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