Question

solve the given system by the substitution method.\

$$\begin{cases}4x + y = 18\\\\7x - 4y = 20\\end{cases}$$

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

Explanation:

Step1: Solve for y from first equation

From \(4x + y = 18\), we get \(y = 18 - 4x\).

Step2: Substitute y into second equation

Substitute \(y = 18 - 4x\) into \(7x - 4y = 20\):
\[

$$\begin{align*} 7x - 4(18 - 4x) &= 20\\ 7x - 72 + 16x &= 20\\ 23x - 72 &= 20\\ 23x &= 20 + 72\\ 23x &= 92\\ x &= \frac{92}{23}\\ x &= 4 \end{align*}$$

\]

Step3: Find y using x = 4

Substitute \(x = 4\) into \(y = 18 - 4x\):
\(y = 18 - 4\times4 = 18 - 16 = 2\)

Answer:

A. The solution is \((4, 2)\)