Method of Elimination
Example:
Solve x + 3y = 11 and 3x + 4y = 18.
Solution:
Given that, x + 3y = 11 --------(1)
3x + 4y = 18 ----------(2)
In the above equations we can not eliminate x and y addition or subtraction
because the coefficients of x and y are different. We use multiplication
property of equality to solve these equation.
If every term in an equation is multiplied with real number the value of the
equation remains unaltered.
Multiply all the terms of the first equation with 3 to make the coefficient
of x equal in both equations.
Equation (1) * 3 = 3x + 9y = 33------(3)
Subtracting the equation (3) from (2), we get
| 3x + 4y = 18 | --------(2) |
| 3x + 9y = 33 | --------(3) |
| Subtracting the equation (3) from (2) |
-5y = -15 |
-5y = -15
y = -15 / -5 = 3
Therefore, y = 3
Substitute y = 3 in one of the equation to find x value.
x + 3y = 11
x + 3 * 3 = 11
x + 9 = 11
x = 11 - 9 = 2
Solution set = {(2,3)}
Verification:
We have to verify the solution (2,3) satisfies both equations or not.
Substitute x = 2 and y = 3 in the given equations.
x + 3y = 11 and 3x + 4y = 18
2 + 3 * 3 = 11 and 3 * 2 + 4 * 3 = 18
2 + 9 = 11 and 6 + 12 = 18
11 = 11 and 18 = 18
Therefore, the solution (2,3) is correct.
Directions: Choose the correct answer. Also write at least ten examples of your own.
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