solve the following system of equations by graphing . If the system is inconsistent or the equations are dependent x+y=6 y-x=6
To solve the system of equations by graphing, we can first rearrange each equation to solve for y:
Equation 1: x + y = 6
y = 6 - x
Equation 2: y - x = 6
y = 6 + x
Now we can graph both equations on the same coordinate plane:
Equation 1: y = 6 - x
Let's choose arbitrary values of x and solve for y:
When x = 0, y = 6 - 0 = 6
When x = 1, y = 6 - 1 = 5
When x = 2, y = 6 - 2 = 4
Plot these points, and draw a line through them:
(0, 6), (1, 5), (2, 4)
Equation 2: y = 6 + x
Again, let's choose arbitrary values of x and solve for y:
When x = 0, y = 6 + 0 = 6
When x = 1, y = 6 + 1 = 7
When x = 2, y = 6 + 2 = 8
Plot these points, and draw a line through them:
(0, 6), (1, 7), (2, 8)
Now, we can see that the lines representing the equations intersect at the point (0, 6). This means that (0, 6) is the solution to the system of equations.
Therefore, the solution to the system of equations is:
x = 0
y = 6