Question

solve the system of equations by the elimination\

$$\begin{cases}4x + 4y = 24\\\\3x - 4y = 11\\end{cases}$$

\select the correct choice below and, if necessar\\(\boldsymbol{\circ}\\) a. the solution is \\(\boldsymbol{\square}\\). (simplify your answe\\(\boldsymbol{\circ}\\) b. there are infinitely many solutions.\\(\boldsymbol{\circ}\\) c. there is no solution.

Explanation:

Step1: Add the two equations

$$(4x + 4y) + (3x - 4y) = 24 + 11$$
$$7x = 35$$

Step2: Solve for x

$$x = \frac{35}{7} = 5$$

Step3: Substitute x=5 into first equation

$$4(5) + 4y = 24$$
$$20 + 4y = 24$$

Step4: Solve for y

$$4y = 24 - 20 = 4$$
$$y = \frac{4}{4} = 1$$

Answer:

A. The solution is $(5, 1)$