Question

1. **consider the system given by \\(\

$$\begin{cases} 3x - 2y = -17 \\\\ 5x + y = 13 \\end{cases}$$

\\) is \\((2, 3)\\) a solution to the system? justify your answer.

Explanation:

Step1: Substitute into first equation

Substitute \(x = 2\), \(y = 3\) into \(3x - 2y\).
\(3(2)-2(3)=6 - 6 = 0\)
The first equation is \(3x - 2y=-17\), but \(0
eq - 17\).

Step2: Substitute into second equation (optional)

Substitute \(x = 2\), \(y = 3\) into \(5x + y\).
\(5(2)+3 = 10 + 3=13\)
The second equation is satisfied, but since the first is not, \((2,3)\) is not a solution.

Answer:

No, \((2,3)\) is not a solution to the system because when substituting \(x = 2\) and \(y = 3\) into the first equation \(3x-2y=-17\), we get \(3(2)-2(3)=0
eq - 17\) (even though it satisfies the second equation \(5x + y = 13\), a solution to the system must satisfy both equations).