What is the solution set of the equations x + y = 10 and x - y = 2? (2023)

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Question: What is the solution set of the equations x + y = 10 and x - y = 2? (2023)

Options:

Correct Answer: (6, 4)

Exam Year: 2023

Solution:

Solving the equations simultaneously gives x = 6 and y = 4, hence the solution set is (6, 4).

What is the solution set of the equations x + y = 10 and x - y = 2? (2023)

What is the solution set of the equations x + y = 10 and x - y = 2? (2023)

Step 1: Write down the two equations: x + y = 10 and x - y = 2.
Step 2: Solve the second equation (x - y = 2) for x: x = y + 2.
Step 3: Substitute the expression for x from Step 2 into the first equation: (y + 2) + y = 10.
Step 4: Combine like terms: 2y + 2 = 10.
Step 5: Subtract 2 from both sides: 2y = 8.
Step 6: Divide both sides by 2: y = 4.
Step 7: Now that we have y, substitute y back into the expression for x: x = 4 + 2.
Step 8: Calculate x: x = 6.
Step 9: The solution set is (x, y) = (6, 4).

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