Question

Solve the system of equations: \[ x + y = 5 \] \[ 2x - y = 4 \]

• A. \( x = 3, y = 2 \)
• B. \( x = 2, y = 3 \)
• C. \( x = 4, y = 1 \)
• D. \( x = 1, y = 4 \)

Hint:

Remember: When solving a system of linear equations, you can use substitution or elimination. Substitution is useful when one of the equations is easily solvable for one variable.

Answer 1

The Correct Option is A

Step 1: Employ substitution or elimination Given system of equations:1. \( x + y = 5 \)2. \( 2x - y = 4 \)We will use the substitution method.Step 2: Isolate a variable From equation 1, \( x + y = 5 \), isolate \( y \):\[y = 5 - x\]Step 3: Substitute into the other equation Substitute \( y = 5 - x \) into equation 2, \( 2x - y = 4 \):\[2x - (5 - x) = 4\]\[2x - 5 + x = 4\]\[3x - 5 = 4\]\[3x = 9\]\[x = 3\]Step 4: Determine the value of \( y \) Substitute \( x = 3 \) back into \( y = 5 - x \):\[y = 5 - 3 = 2\]Solution: The system of equations is solved by \( x = 3 \) and \( y = 2 \). This corresponds to option (1).