Find the solution to the system of equations by graphing

Question

Y=6 - c and y=x - 2

Answer 1

To graph the system of equations, we will create a graph for each equation and see where they intersect.

1) Start with the equation y = 6 - c:
To graph this equation, we need to remember that the y-intercept is 6. Therefore, plot a point at (0, 6) on the graph. From this point, we can find another point by following the slope of -1. This means that for every increase of 1 in x, y decreases by 1.

2) Now, look at the equation y = x - 2:
Again, we find that the y-intercept is -2. Plot a point at (0, -2) on the graph. From this point, follow the slope of 1 to find another point. This means for every increase of 1 in x, y increases by 1.

3) Plot these two points on a graph and draw a line passing through them. The point at which the lines intersect is the solution to the system of equations.

(Note: I apologize for the confusion regarding the variable "c" in the first equation. It is not clear if it is meant to be a variable or a constant. I have treated it as a constant for the purpose of graphing.)

Here is a visual representation of the graphed equations:

|
7 | .
| .
6 | .
| .
5 | .
| .
4 | .
| .
3 | .
| .
2 | .
| .
1 | .
| .
0 |_____________________________________
0 1 2 3 4 5 6 7 8

As seen from the graph, the lines intersect at the point (4, 2). Therefore, the solution to the system of equations is x = 4 and y = 2.