Question

solve the system of equations by the addition method.\

$$\begin{cases}20x = -11y + 60\\\\4x + 4y = 12\\end{cases}$$

\select the correct choice below and, if necessary, fill in the answer box to complete your choice.\\(\boldsymbol{\circ}\\) a. the solution is \\(\square\\). (simplify your answer. type an ordered pair.)\\(\boldsymbol{\circ}\\) b. there is an infinite number of solutions.\\(\boldsymbol{\circ}\\) c. there is no solution.

Explanation:

Step1: Rewrite the first equation

Rewrite \(20x = -11y + 60\) in standard form \(20x + 11y = 60\).

Step2: Multiply the second equation

Multiply \(4x + 4y = 12\) by \(5\) to get \(20x + 20y = 60\).

Step3: Subtract the equations

Subtract \(20x + 11y = 60\) from \(20x + 20y = 60\):
\[

$$\begin{align*} (20x + 20y) - (20x + 11y) &= 60 - 60\\ 20x + 20y - 20x - 11y &= 0\\ 9y &= 0\\ y &= 0 \end{align*}$$

\]

Step4: Substitute y into an equation

Substitute \(y = 0\) into \(4x + 4y = 12\):
\[

$$\begin{align*} 4x + 4(0) &= 12\\ 4x &= 12\\ x &= 3 \end{align*}$$

\]

Answer:

A. The solution is \((3, 0)\)