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Two Variable Equation Examples

Two Variable Equation Example 1

Question
Using the elimination method to solve the group of equations 2x - y = 4 and 2x + y = 8.
Solution
Solve these two variables equation
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.

Two Variable Equation Example 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.