What is the solution set of the system #4x+y=12# and #15x+y=45#?
2 Answers
Explanation:
Equation (1):
Equation (2):
Substitute
Explanation:
There are different ways to solve this. The easiest way (probably) is to add or subtract each equation with each other and get rid of either the
In this case it is easiest to take the second equation and subtract it by the first:
Equation (2) - Equation (1)
Simplify
Then substitute this answer into Equation (1) to get
Another (more complex) way to answer is to use matrix multiplication .
The system of euquations can be rewritten in matrix form:
Become
Now we need to inverse the left hand matrix to isolate the
where
To solve this system we need to get the inverse of
If
For
Now we can solve the problem as we can substitute this into the equation
We multiply out the matrices and get the following result:
This gives us the answer for