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# Two Variable Equation Examples

# Two Variable Equation Example 1

# Two Variable Equation Example 2

- Question
- Using the elimination method to solve the group of equations 2x - y = 4 and 2x + y = 8.

- Solution

- Since the y terms in the equations are negatives of each other so we use the elimination method.
- By add equations (1) and (2), we eliminate the variable y, and get x = 3.
- Then we substitute 3 for x in the equation (2) to get y = 2.
- Check if the answers are correct, we replace x by 3 and y by 2 in the original equations:
- 2x - y = 2(3) - 2 = 6 - 2 = 4
- 2x + y = 2(3) + 2 = 6 + 2 = 8, which satisfy the original equations,
- Therefore, the solution is x = 3 and y = 2.

- Question
- Using the substitution method to solve the group of equations 5x + y = 9 and 2x - 3y = 7.

- Solution
- 5x + y = 9 ...equation1
- 2x - 3y = 7 ...equation2
- from equation1, express y interms of x
- y = 9 - 5x ...equation3
- substitute equation3 into equation2
- 2x - 3(9 - 5x) = 7
- remove parenthesis
- 2x - 27 + 15x = 7
- move numbers to the right side of the equation
- 2x + 15x = 27 + 7
- combine similar (like) terms
- 17x = 34
- x = 2
- y = 9 - 5x = 9 -5 × 2 = 9 - 10 = -1
- so x = 2 and y = -1

- Check if the answers are correct,
- we replace x by 2 and y by -1 in the original equations:
- 5(2) + (-1) = 10 - 1 = 9
- 2(2) - 3(-1) = 4 + 3 = 7
- Therefore, the solution is x = 2 and y = -1.