Questions: Solve the system of equations by the substitution method. x+y = 20 y = 4x Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution of the system is ☐ (Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression.) B. There are infinitely many solutions. C. There is no solution.

Solution Steps

To solve the system of equations using the substitution method, we start by substituting the expression for \( y \) from the second equation into the first equation. This will allow us to solve for \( x \). Once we have the value of \( x \), we can substitute it back into the expression for \( y \) to find the corresponding value of \( y \). This will give us the solution as an ordered pair \((x, y)\).

We start with the system of equations: \[ \begin{aligned}

1. & \quad x + y = 20 \\
2. & \quad y = 4x \end{aligned} \] Substituting the expression for \( y \) from the second equation into the first equation gives: \[ x + 4x = 20 \]

Combining like terms, we have: \[ 5x = 20 \] Dividing both sides by 5 results in: \[ x = 4 \]

Now, substituting \( x = 4 \) back into the second equation to find \( y \): \[ y = 4(4) = 16 \]

Final Answer