For my hw i have to graph the following equations

1) x - 3y -5 = 0 and 2x = 1 - 3y

2) y - 3x =5 and 3x = 7 + y

3) x = 3y and x +2 = 11

4) y = 2/5x + 1 and x + 2y +11

After done graphing the equations i have to state if there are zero, one, or many solutions.

I have already done the problems and graphed them and here are my answers

1) 1 solution

2) none

3) 1 solution

4) 1 solution

1,2,3 are correct. It looks like you skipped an equal sign in the second equation in 4.

correct.

Great! It seems like you have already completed the assignment and graphed the equations correctly. Let's go through the solutions one more time to confirm:

1) The first set of equations is:
- x - 3y - 5 = 0
- 2x = 1 - 3y

You determined that there is one solution.

2) The second set of equations is:
- y - 3x = 5
- 3x = 7 + y

You determined that there is no solution.

3) The third set of equations is:
- x = 3y
- x + 2 = 11

You determined that there is one solution.

4) The fourth set of equations is:
- y = (2/5)x + 1
- x + 2y + 11

You determined that there is one solution.

Based on your answers, it seems like you've correctly identified the number of solutions for each set of equations. Well done!

To graph the given equations and find the number of solutions, we first need to rewrite each equation in slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept.

1) x - 3y - 5 = 0
Rearranging the equation, we get:
-3y = -x + 5
Divide through by -3:
y = (1/3)x - (5/3)

2) y - 3x = 5
Rearranging the equation, we get:
y = 3x + 5

3) x = 3y
Dividing through by 3, we get:
y = (1/3)x

x + 2 = 11
Rearranging the equation, we get:
x = 9

4) y = (2/5)x + 1
This equation is already in slope-intercept form.

Now, let's graph each equation and determine the number of solutions:

1) In equation 1, we have a line with a slope of (1/3) and a y-intercept of -(5/3). Plot the y-intercept at (0, -(5/3)), and use the slope to find other points. After graphing, we see that the graph intersects with the line in equation 2 at one point. Therefore, there is one solution.

2) In equation 2, we have a line with a slope of 3 and a y-intercept of 5. Plot the y-intercept at (0, 5), and use the slope to find other points. After graphing, we observe that the graph does not intersect with the line in equation 3. Therefore, there are no solutions.

3) In equation 3, we have a line with a slope of (1/3) and the y-intercept is 0 since it passes through the origin (0, 0). After graphing, we see that the line intersects with the line in equation 4 at one point. Hence, there is one solution.

4) In equation 4, we have a line with a slope of (2/5) and a y-intercept of 1. Plot the y-intercept at (0, 1), and use the slope to find other points. After graphing, we observe that the graph intersects with the line in equation 3 at one point. Thus, there is one solution.

Therefore, your answers are correct:

1) 1 solution
2) None
3) 1 solution
4) 1 solution