Question

solve the system of equations and write the solution as an ordered pair\\
\\(\

$$\begin{cases} x - 3y = 2 \\\\ 5x + 2y = 44 \\end{cases}$$

\\)\\
the ordered pair that satisfies both equations is ( , )

Explanation:

Step1: Solve the first equation for \( x \)

From \( x - 3y = 2 \), we can express \( x \) as \( x = 3y + 2 \).

Step2: Substitute \( x = 3y + 2 \) into the second equation

Substitute \( x \) into \( 5x + 2y = 44 \):
\[

$$\begin{align*} 5(3y + 2) + 2y &= 44\\ 15y + 10 + 2y &= 44\\ 17y + 10 &= 44 \end{align*}$$

\]

Step3: Solve for \( y \)

Subtract 10 from both sides:
\[
17y = 44 - 10 = 34
\]
Divide both sides by 17:
\[
y = \frac{34}{17} = 2
\]

Step4: Substitute \( y = 2 \) back into \( x = 3y + 2 \)

\[
x = 3(2) + 2 = 6 + 2 = 8
\]

Answer:

The solution to the system of equations is \( x = 8 \) and \( y = 2 \), so the ordered pair is \( (8, 2) \).