I have been asked a question regarding inconsistency. How would I use these equations to solve the questions?
x-y=5
2x = 2y+14
If you arrange your second equation this way
2x - 2y = 14 then divide by 2 you get
x-y=7
compare this with your first equation
You are looking at two lines which are parallel, and therefore can never intersect.
This is what makes the two equations "inconsistent"
To solve the system of equations x - y = 5 and 2x = 2y + 14, you can use the method of substitution or elimination.
Let's start with the method of substitution.
1. Solve one of the equations for one variable in terms of the other variable.
From the first equation, we can solve for x: x = y + 5.
2. Substitute the expression obtained in step 1 into the other equation.
Using the expression x = y + 5, we substitute it into the second equation: 2(y + 5) = 2y + 14.
3. Simplify and solve the resulting equation for the remaining variable.
Expanding and simplifying the equation, we get: 2y + 10 = 2y + 14.
Since the variable y cancels out, we are left with 10 = 14, which is not true.
Since the equation is inconsistent, this means that there is no solution to the system of equations.
Now, let's understand why these equations are inconsistent through a graphical interpretation.
The first equation x - y = 5 can be rearranged to y = x - 5, which represents a straight line with a slope of 1 and a y-intercept of -5.
The second equation 2x = 2y + 14 can be rearranged to x - y = 7, which also represents a straight line with a slope of 1 and a y-intercept of -7.
When we plot these two lines on a graph, we can see that they are parallel and will never intersect.
A system of equations is inconsistent when the lines representing the equations are parallel, indicating that there is no solution that satisfies both equations simultaneously.