Solve the system of linear equations by graphing

3x+y=0
2x-y=5
Graph the system
What is the solution of the system of equations?

To solve the system of linear equations by graphing, we need to plot both equations on a coordinate plane and find the point of intersection, which represents the solution to the system.

First, let's rewrite the equations in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.

Equation 1: 3x + y = 0
Rearranging, we get: y = -3x

Equation 2: 2x - y = 5
Rearranging, we get: y = 2x - 5

Now, we can graph the system by plotting the two lines on the same coordinate plane.

For Equation 1 (y = -3x):
- Start at the y-intercept (0, 0).
- Find additional points by selecting values for x, substituting them into the equation to determine corresponding y-values.
- Connect the points to form a straight line.

For Equation 2 (y = 2x - 5):
- Start at the y-intercept (-5, 0).
- Find additional points using the same process as above.
- Connect the points to form another straight line.

Once the lines are plotted, find the point where they intersect. This point represents the solution to the system of equations.

To determine the coordinates of the intersection point, you can read it directly from the graph or calculate it precisely using the intersection point feature of some graphing software or a graphing calculator.

Once you have the intersection point, you can determine the solution to the system of equations by identifying the x and y values at that point.