Final answer:
To solve this system of linear equations by graphing, plot the graphs for each equation and find the point of intersection.
Step-by-step explanation:
To solve this system of linear equations by graphing, we need to graph each equation and find the point of intersection.
First, we graph the equation 3y + 4x = 3:
Solve for y:
3y = -4x + 3
y = (-4/3)x + 1
Plot points:
When x = 0, y = 1
When x = 3, y = -1
Draw the line passing through these two points.
Next, we graph the equation x + 3y = -6:
Solve for y:
3y = -x - 6
y = (-1/3)x - 2
Plot points:
When x = 0, y = -2
When x = -3, y = -1
Draw the line passing through these two points.
The point of intersection between the two lines is (-3, -1).
Therefore, the solution to the system of linear equations is x = -3 and y = -1.