Question

Solve the following simultaneous equations: \[ x + y = 4 \quad \text{and} \quad 2x - y = 2 \]

Hint:

To solve simultaneous equations, use elimination or substitution. Adding or subtracting equations helps eliminate one variable easily.

Answer 1

Step 1: Write the given equations.
\[ \text{(I)} \; x + y = 4 \] \[ \text{(II)} \; 2x - y = 2 \] Step 2: Add equations (I) and (II) to eliminate \(y\).
\[ (x + y) + (2x - y) = 4 + 2 \] \[ 3x = 6 \] Step 3: Solve for \(x\).
\[ x = \frac{6}{3} = 2 \] Step 4: Substitute \(x = 2\) in equation (I).
\[ 2 + y = 4 \implies y = 2 \] Step 5: Conclusion.
Hence, the solution of the given simultaneous equations is \(x = 2, \; y = 2.\)
Final Answer: \[ \boxed{x = 2, \; y = 2} \]