Question

If \(3x + 4y = 12\) and \(x - y = 1\), what is the value of \(x + y\)?

• A. \(\dfrac{25}{7}\)
• B. \(\dfrac{16}{7}\)
• C. \(\dfrac{9}{7}\)
• D. \(\dfrac{7}{2}\)

Hint:

When solving a system of linear equations, always simplify and verify values step-by-step. Adjust answer choices to match rational results if necessary.

Answer 1

The Correct Option is A

Step 1: Start with the system of equations:
\[ (1) \ 3x + 4y = 12, \quad (2) \ x - y = 1 \] Step 2: Solve equation (2) for \(x\):
\[ x = y + 1 \] Step 3: Substitute into equation (1):
\[ 3(y + 1) + 4y = 12 \] \[ 3y + 3 + 4y = 12 \Rightarrow 7y = 9 \Rightarrow y = \frac{9}{7} \] Step 4: Now compute \(x\):
\[ x = \frac{9}{7} + 1 = \frac{16}{7} \] Step 5: Then \(x + y = \frac{16}{7} + \frac{9}{7} = \frac{25}{7}\).
Step 6: Therefore, the correct value of \(x + y\) is \(\boxed{\frac{25}{7}}\).
Step 7: This matches option (a).