solve the system of equation by graphing. then classify the system.
x + y=10
x - y=2
use this page
http://rechneronline.de/function-graphs/
enter
10-x for first function
x+2 for the 2nd function
change the "range x-axis from" to -10 to +10
To solve the system of equations by graphing, we can plot the graphs of the two equations on the same coordinate plane and then determine the point of intersection. The point where the two graphs intersect is the solution to the system.
Let's start by rearranging each equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:
Equation 1: x + y = 10
Rearrange as: y = -x + 10
Equation 2: x - y = 2
Rearrange as: y = x - 2
Now, let's graph these equations:
For equation 1 (y = -x + 10):
- Plot the y-intercept at (0, 10).
- Use the slope (-1) to find another point. From the y-intercept, move one unit down (change in y) and one unit to the right (change in x). Plot this point at (1, 9).
- Connect the two points with a straight line.
For equation 2 (y = x - 2):
- Plot the y-intercept at (0, -2).
- Use the slope (1) to find another point. From the y-intercept, move one unit up (change in y) and one unit to the right (change in x). Plot this point at (1, -1).
- Connect the two points with a straight line.
Now that we have graphed both equations, we can see that the lines intersect at the point (4, 6). This means the solution to the system of equations is x = 4 and y = 6.
To classify the system, we can observe that the lines intersect at a unique point. Thus, the system is classified as consistent and independent.