College Math Placement Practice Test

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What is the solution to the system of equations: 2x + 3y = 6 and x - y = 2?

x = 2, y = 0
x = 3, y = 2
x = 3, y = 0
x = 1, y = 1

The correct answer is: x = 3, y = 0

To solve the system of equations 2x + 3y = 6 and x - y = 2, we can use substitution or elimination. Here, we'll use substitution for clarity. First, solve the second equation x - y = 2 for x: x = y + 2. Next, substitute this expression for x into the first equation: 2(y + 2) + 3y = 6. Now, distribute the 2: 2y + 4 + 3y = 6. Combine like terms: 5y + 4 = 6. Subtract 4 from both sides: 5y = 2. Now, divide both sides by 5: y = 2/5. Next, substitute y back into the equation x = y + 2 to find x: x = (2/5) + 2 = (2/5) + (10/5) = 12/5. Thus, the solution to the system is x = 12/5 and y = 2/5. Evaluating the provided choices, we find that option C (x = 3, y = 0) does not correctly reflect the solution we derived. The