Question

the linear system

\\
\

$$\begin{aligned} 4x + 6y &= 50 \\\\ 8x + 7y &= 65 \\end{aligned}$$

\\

is rewritten as the following augmented matrix:

\\
\left\

$$\begin{array}{cc|c} 4 & 6 & 50 \\\\ 8 & 7 & 65 \\end{array}$$

\
ight
\\

solve for \\(x\\) and \\(y\\).

\\(x =\\)

\\(y =\\)

Explanation:

Step1: Write the system of equations

$$
LATEXBLOCK0
$$

Step2: Eliminate \(x\) by multiplying the first equation

$$8x + 12y = 100$$

Step3: Subtract the second equation from the new equation

$$(8x + 12y) - (8x + 7y) = 100 - 65$$

Step4: Solve for \(y\)

$$5y = 35 \implies y = 7$$

Step5: Substitute \(y\) back to solve for \(x\)

$$4x + 6(7) = 50 \implies 4x + 42 = 50 \implies 4x = 8 \implies x = 2$$

Answer:

\(x = 2\)
\(y = 7\)