Question

solve the system of equations. if the system has no solution, say that it is inconsistent. graph the lines of the system.
\

$$\begin{cases} 4x - y = 2 \\ 3x + 2y = 18 \\end{cases}$$

select the correct choice below and, if necessary, fill in any answer boxes within your choice.
\bigcirc a. the solution is x = \square and y = \square.
(type integers or simplified fractions.)
\bigcirc b. there are infinitely many solutions. using ordered pairs, they can be expressed as \\{(x,y) \mid x = \square, y is any real number\\}.
(simplify your answer. type an expression using y as the variable as needed.)
\bigcirc c. the system is inconsistent.

Explanation:

Step1: Solve for y from first equation

From \(4x - y = 2\), we can rewrite it as \(y = 4x - 2\).

Step2: Substitute y into second equation

Substitute \(y = 4x - 2\) into \(3x + 2y = 18\):

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Step3: Find y using x = 2

Substitute \(x = 2\) into \(y = 4x - 2\):
\(y = 4(2) - 2 = 8 - 2 = 6\)

Answer:

A. The solution is \(x = 2\) and \(y = 6\).