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: Use the substitution or elimination method We are given the system of equations: 1. \( x + y = 5 \) 2. \( 2x - y = 4 \) We will use the substitution method. Step 2: Solve one equation for one variable From the first equation \( x + y = 5 \), solve for \( y \): \[ y = 5 - x \] Step 3: Substitute into the second equation Substitute \( y = 5 - x \) into the second equation \( 2x - y = 4 \): \[ 2x - (5 - x) = 4 \] \[ 2x - 5 + x = 4 \] \[ 3x - 5 = 4 \] \[ 3x = 9 \] \[ x = 3 \] Step 4: Solve for \( y \) Now substitute \( x = 3 \) back into \( y = 5 - x \): \[ y = 5 - 3 = 2 \] Answer: Therefore, the solution to the system of equations is \( x = 3 \) and \( y = 2 \). So, the correct answer is option (1).