Question

Solve the system of equations: \[ x + y = 10 \] \[ 3x - y = 5 \]

• A. \( x = 5, y = 5 \)
• B. \( x = 4, y = 6 \)
• C. \( x = 3, y = 7 \)
• D. \( x = 6, y = 4 \)

Hint:

Remember: When solving a system of equations, either substitution or elimination methods can be used. Make sure to carefully check your calculations when performing algebraic steps.

Answer 1

The Correct Option is A

Step 1: Use the substitution or elimination method We are given the system of equations: 1. \( x + y = 10 \) 2. \( 3x - y = 5 \) We will use the elimination method. First, add both equations to eliminate \( y \). Step 2: Add the two equations Add equation 1 and equation 2: \[ (x + y) + (3x - y) = 10 + 5 \] Simplify: \[ x + 3x = 15 \] \[ 4x = 15 \] \[ x = \frac{15}{4} = 3.75 \] Step 3: Substitute \( x = 3.75 \) back into the first equation Substitute \( x = 3.75 \) into the first equation \( x + y = 10 \): \[ 3.75 + y = 10 \] \[ y = 10 - 3.75 = 6.25 \] Answer: Therefore, the solution to the system of equations is \( x = 3.75 \) and \( y = 6.25 \). So, the correct answer is option (2).