Use an elimination strategy to solve this linear system:
10x + 10y = 1030
5x + 5y = 135
These two lines are parallel and distinct, hence there are no solutions.
Show that this is the case by dividing the first one by two to get
5x+5y=515
Since both equations have 5x+5y on the left, and different values on the right, it shows that the two lines are parallel and distinct => no solutions.
To solve this linear system using the elimination strategy, we need to eliminate one of the variables by multiplying one or both equations by appropriate constants. Here's how you can proceed:
Step 1: Multiply the second equation by 2 to make the coefficients of y in both equations the same. This will allow us to eliminate y later.
2(5x + 5y) = 2(135)
10x + 10y = 270
Now we have the following system:
10x + 10y = 1030
10x + 10y = 270
Step 2: Subtract the second equation from the first equation to eliminate the variable y.
(10x + 10y) - (10x + 10y) = 1030 - 270
10x + 10y - 10x - 10y = 760
0 = 760
When we subtract the two equations, we get 0 = 760. This means there are no values of x and y that satisfy both equations simultaneously.
Therefore, this linear system is inconsistent and does not have a solution.