Question

determine the solution of the system of equations.\

$$\begin{cases}3x + 2y = 9\\\\4x - y = 34\\end{cases}$$

\
enter the correct answer in the boxes.\
(\boxed{ }, \boxed{ })

Explanation:

Step1: Solve the second equation for y

From \(4x - y = 34\), we can rewrite it as \(y = 4x - 34\).

Step2: Substitute y into the first equation

Substitute \(y = 4x - 34\) into \(3x + 2y = 9\):
\[

$$\begin{align*} 3x + 2(4x - 34)&= 9\\ 3x + 8x - 68&= 9\\ 11x - 68&= 9\\ 11x&= 9 + 68\\ 11x&= 77\\ x&= \frac{77}{11}\\ x&= 7 \end{align*}$$

\]

Step3: Find y using x = 7

Substitute \(x = 7\) into \(y = 4x - 34\):
\[

$$\begin{align*} y&= 4\times7 - 34\\ y&= 28 - 34\\ y&= -6 \end{align*}$$

\]

Answer:

\((7, -6)\)