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### Middle/High School Algebra, Geometry, and Statistics (AGS)1.20 Solving Equations - Elimination Method II

#### 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.
 Q 1: Solve 3x + 2y = 27 and x + y = 10.x = 7 and y = 3x = 4 and y = 8x = 3 and y = 7x = 8 and y = 4 Q 2: Solve x + 2y = 10 and 3x + 4y = 22.x = 2 and y = 4x = 4 and y = 2x = 3 and y = 4x = 3 and y = 3 Question 3: This question is available to subscribers only! Question 4: This question is available to subscribers only!

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