Question

solve the system of equations by substitution. when solving, x = 3 is obtained.
\\(\

$$\begin{align*} y &= 4x\\\\ -2x + y &= 6 \\end{align*}$$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\\(\boldsymbol{\circ}\\) a. the solution is \\(\square\\).
\\(\quad\\) (type an ordered pair. simplify your answer. use integers or fractions for any numbers in the)
\\(\boldsymbol{\circ}\\) b. there are infinitely many solutions.
\\(\boldsymbol{\circ}\\) c. there is no solution.

Explanation:

Step1: Substitute \( y = 4x \) into the second equation

We have the second equation \( -2x + y = 6 \). Substitute \( y = 4x \) into it, we get \( -2x + 4x = 6 \).

Step2: Solve for \( x \)

Simplify the left - hand side of the equation \( -2x + 4x = 6 \), we have \( 2x = 6 \). Divide both sides by 2, \( x=\frac{6}{2}=3 \), which matches the given \( x = 3 \).

Step3: Find the value of \( y \)

Since \( y = 4x \) and \( x = 3 \), substitute \( x = 3 \) into \( y = 4x \), we get \( y=4\times3 = 12 \).

Answer:

A. The solution is \((3,12)\)