Consider the following system of equations.
y=2x-2
y-2x=9
What can you conclude about the system of equations?
a. The system of equations is inconsistent.
b. The system of equations is dependent.
c. The system of equations is independent.
d. none of these.
if you set them up in a standard way, you have
2x-y = 2
2x-y = -9
(a) both cannot be true
To determine what can be concluded about the system of equations, we need to solve the equations and analyze the results.
The given system of equations is:
y = 2x - 2 ...(Equation 1)
y - 2x = 9 ...(Equation 2)
1. To solve for y, we can substitute Equation 1 into Equation 2:
(2x - 2) - 2x = 9
Simplifying, we get:
-2 = 9
2. The equation -2 = 9 is not true, which means there is no common solution for x and y that satisfies both equations.
3. Therefore, the system of equations is inconsistent because there is no solution that satisfies both equations.
The correct answer is:
a. The system of equations is inconsistent.