Final Answer:
The coordinate plane with the two lines -3x + 3y = 3 and 5x - y = 13 is shown below:
Step-by-step explanation:
To draw the coordinate plane, we first need to determine the slope and y-intercept of each line.
The first line, -3x + 3y = 3, has a slope of -3/3 = -1 and a y-intercept of 3. We can write this line as:
y = -x + 3
The second line, 5x - y = 13, has a slope of 5/1 = 5 and a y-intercept of 13. We can write this line as:
y = 5x - 13
Next, we need to find the point of intersection of the two lines. To do this, we can set the equations equal to each other and solve for x and y.
y = -x + 3 y = 5x - 13
We can solve for x by adding the two equations together:
2y = -x + 3 + 5x - 13 2y = -x + 16
Solving for x, we get:
x = 8
Now that we have found the point of intersection (x, y) = (8, 16), we can draw the line on the coordinate plane.
To draw the line, we simply connect the point of intersection (8, 16) to the y-axis and the x-axis.