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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.

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.