Question

The solution of \( 2x + 3y = 18 \); \( x - 2y = 2 \) will be:

• A. \( x = 6, y = 2 \)
• B. \( x = 3, y = 4 \)
• C. \( x = 3, y = 8 \)
• D. \( x = 0, y = 6 \)

Hint:

In the substitution method, solving one equation for a variable and then substituting it into the other equation simplifies finding the solution.

Answer 1

The Correct Option is B

Step 1: Write the system of equations.
We are given the system of equations: \[ 2x + 3y = 18 \quad \text{(1)} \] \[ x - 2y = 2 \quad \text{(2)} \] We will use the substitution method to solve this system.
Step 2: Solve for \( x \) in equation (2).
From equation (2), solve for \( x \): \[ x = 2 + 2y \quad \text{(3)} \]
Step 3: Substitute the value of \( x \) into equation (1).
Substitute the expression for \( x \) from equation (3) into equation (1): \[ 2(2 + 2y) + 3y = 18 \] Simplify: \[ 4 + 4y + 3y = 18 \] \[ 4 + 7y = 18 \] Subtract 4 from both sides: \[ 7y = 14 \] \[ y = 2 \]
Step 4: Substitute \( y = 2 \) into equation (2).
Now substitute \( y = 2 \) back into equation (2): \[ x - 2(2) = 2 \] \[ x - 4 = 2 \] Add 4 to both sides: \[ x = 6 \]
Step 5: Conclusion.
Thus, the solution to the system of equations is \( x = 6 \) and \( y = 2 \). Therefore, the correct answer is (A), not (B).