Find the solution to the system of equations by graphing Y equals six minus X and Y equals X -2
To solve the system of equations by graphing, we need to graph both equations on the same coordinate plane and find the point where the two lines intersect.
First, let's graph the equation Y = 6 - X:
For this equation:
- When X = 0, Y = 6 - 0 = 6. So, one point is (0, 6).
- When X = 6, Y = 6 - 6 = 0. So, another point is (6, 0).
Plot these two points and draw a straight line passing through them. This line represents the equation Y = 6 - X.
Now, let's graph the equation Y = X - 2:
For this equation:
- When X = 0, Y = 0 - 2 = -2. So, one point is (0, -2).
- When X = 4, Y = 4 - 2 = 2. So, another point is (4, 2).
Plot these two points and draw a straight line passing through them. This line represents the equation Y = X - 2.
The graph should demonstrate two lines intersecting at a point. The coordinates of this point are the solution to the system of equations.
Upon observing the graph, it can be seen that the lines intersect at the point (2, 4).
Therefore, the solution to the system of equations is X = 2 and Y = 4.
To solve the system of equations by graphing, let's plot the lines represented by each equation on the same graph:
1. Equation 1: y = 6 - x
- Choose a value for x and calculate its corresponding y.
- For example, when x = 0, y = 6 - 0 = 6.
- Plot the point (0, 6).
- Repeat this process for a few more x values to get additional points.
- Connect the plotted points to obtain the line.
2. Equation 2: y = x - 2
- Again, choose values for x and calculate y.
- For x = 0, y = 0 - 2 = -2.
- Plot the point (0, -2).
- Repeat this process for a few more x values to get additional points.
- Connect the plotted points to obtain the second line.
By graphing the two equations, you would find that the lines intersect at the point (4, 2). Therefore, the solution to the system of equations is x = 4 and y = 2.