can you show the problems worked out
x-y=3 if x=1,2,3,4 etc... and -x+4y=9 if x = 1,2,3,45,6 etc.. I need to graph coordinates. Thanks
Certainly! To graph the given equations, you can start by creating a table of values for each equation using the given values of x. Then, plot these points on a graph to visualize the coordinates.
1. Equation: x - y = 3
Let's substitute x = 1, 2, 3, 4, and find the corresponding values of y:
For x = 1:
1 - y = 3
-y = 2
y = -2
So, the first point is (1, -2).
For x = 2:
2 - y = 3
-y = 1
y = -1
The second point is (2, -1).
For x = 3:
3 - y = 3
-y = 0
y = 0
The third point is (3, 0).
For x = 4:
4 - y = 3
-y = -1
y = 1
The fourth point is (4, 1).
Now, you can plot these points on a graph.
2. Equation: -x + 4y = 9
Substitute x = 1, 2, 3, 4, and find the corresponding values of y:
For x = 1:
-1 + 4y = 9
4y = 10
y = 2.5
So, the first point is (1, 2.5).
For x = 2:
-2 + 4y = 9
4y = 11
y = 2.75
The second point is (2, 2.75).
For x = 3:
-3 + 4y = 9
4y = 12
y = 3
The third point is (3, 3).
For x = 4:
-4 + 4y = 9
4y = 13
y = 3.25
The fourth point is (4, 3.25).
Now, plot these points on the same graph.
Once you have plotted the points for both equations on the graph, you can connect these points to visualize the lines corresponding to each equation. The point where these lines intersect is the solution to the system of equations, if any.