Question

use the graph to solve the system.
$y = 3x + 5$
$y = -2x - 5$

Explanation:

Step1: Recall system solution via graph

The solution to a system of linear equations \(y = 3x + 5\) and \(y=-2x - 5\) (wait, correction: the second equation is \(y=-2x - 5\)? Wait, the graph shows the two lines intersecting. The solution of a system of linear equations graphed is the point of intersection \((x,y)\) where both equations are satisfied.

Step2: Identify intersection point

From the graph, we look for the point where the two lines \(y = 3x+5\) and \(y=-2x - 5\) (wait, maybe typo in original, but looking at the graph, let's check coordinates. Let's assume the intersection is at \(x=-2\), \(y=-1\)? Wait, no, let's re - examine. Wait, the equations are \(y = 3x + 5\) and \(y=-2x - 5\)? Wait, no, the user wrote \(y=-2x - 5\)? Wait, the original problem has \(y = 3x + 5\) and \(y=-2x - 5\)? Wait, the graph: let's find the intersection. Let's suppose the two lines cross at \(x=-2\), \(y=-1\)? Wait, no, let's solve the system algebraically to check. Set \(3x + 5=-2x-5\), \(3x + 2x=-5 - 5\), \(5x=-10\), \(x = - 2\), then \(y=3(-2)+5=-6 + 5=-1\). So the intersection point is \((-2,-1)\). So the solution to the system is \(x=-2\), \(y = - 1\).

Answer:

The solution to the system \(

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

\) is \(x=-2,y=-1\) or the ordered pair \((-2,-1)\)