College Math Placement Practice Test

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.

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