Questions: Solve the system by the substitution method. x+y = 8 y = 3x

Transcript text: Solve the system by the substitution method. \[ \begin{aligned} x+y & =8 \\ y & =3 x \end{aligned} \]

Solution

Solution Steps

Step 1: Substitute \( y = 3x \) into the first equation

The system of equations is: \[ \begin{aligned} x + y &= 8 \\ y &= 3x \end{aligned} \] Substitute \( y = 3x \) into the first equation: \[ x + 3x = 8 \]

Step 2: Solve for \( x \)

Combine like terms: \[ 4x = 8 \] Divide both sides by 4: \[ x = 2 \]

Step 3: Solve for \( y \)

Substitute \( x = 2 \) into \( y = 3x \): \[ y = 3(2) = 6 \]

Final Answer

The solution is the ordered pair \( (2, 6) \). Therefore, the correct choice is: \[ \boxed{\text{A. The solution is } (2, 6)} \]

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