Question

solve the system of equations by the elimination method\\
\\(\

$$\begin{cases}4x + 4y = 34\\\\3x - 4y = 11\\end{cases}$$

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

Explanation:

Step1: Eliminate y variable

Multiply the second equation by 2:
$$2*(3x - 4y) = 2*11 \implies 6x - 8y = 22$$
Add to first equation:
$$(4x + 8y) + (6x - 8y) = 28 + 22$$
$$10x = 50$$

Step2: Solve for x

Divide both sides by 10:
$$x = \frac{50}{10} = 5$$

Step3: Substitute x to find y

Plug $x=5$ into $3x - 4y = 11$:
$$3*5 - 4y = 11 \implies 15 - 4y = 11$$
$$-4y = 11 - 15 \implies -4y = -4$$
$$y = \frac{-4}{-4} = 1$$

Answer:

A. The solution is $\boldsymbol{(5, 1)}$