Do y=x-4 and 2x-2y=5 have one, none , or infinite solutions?
To determine the number of solutions for this system of equations, we can solve them simultaneously. Let's start by solving them using the method of substitution.
First, we have the equation y = x - 4. We can substitute this expression into the second equation, which is 2x - 2y = 5.
Substituting y = x - 4 into the second equation, we get:
2x - 2(x - 4) = 5
Simplifying the equation, we have:
2x - 2x + 8 = 5
8 = 5
As 8 is not equal to 5, we have reached a contradiction, indicating that the system is inconsistent. In other words, there are no solutions to this system of equations.
Therefore, the answer is that the system has no solutions.
WHat do you think?
If you use the method of substitution and sub y=x-4 into the other equation you get an 'interesting' result. What does the result tell you about the number of solutions?