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: Employ the substitution or elimination method Given the system of equations:1. \( x + y = 10 \)2. \( 3x - y = 5 \)The elimination method will be applied. First, add both equations to eliminate \( y \).Step 2: Sum the two equations Sum equation 1 and equation 2:\[(x + y) + (3x - y) = 10 + 5\]Simplify the expression:\[x + 3x = 15\]\[4x = 15\]\[x = \frac{15}{4} = 3.75\]Step 3: Substitute \( x = 3.75 \) 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: The solution to the system of equations is \( x = 3.75 \) and \( y = 6.25 \). This corresponds to option (2).