Solve using linear combinations.
x - 5y = 6
3x + 4y = 18
What are linear combinations?
Since this is not my area of expertise, I searched Google under the key words "linear combinations" to get these possible sources:
http://www.google.com/search?client=safari&rls=en&q=linear+combinations&ie=UTF-8&oe=UTF-8
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/
Linear combinations refer to a method of solving a system of linear equations by adding or subtracting multiples of the equations in order to eliminate one variable at a time.
In the given example equations:
1) x - 5y = 6
2) 3x + 4y = 18
To solve the system using linear combinations, we need to manipulate the equations so that when they are added or subtracted, one of the variables will cancel out.
Let's multiply equation 1 by 3 and equation 2 by 1, so that the coefficients of x in both equations become the same (3x). This will allow us to easily cancel out the x term when we subtract the equations.
3(x - 5y) = 3(6) --> 3x - 15y = 18
1(3x + 4y) = 1(18) --> 3x + 4y = 18
Now, we can subtract the two equations:
(3x - 15y) - (3x + 4y) = 18 - 18
-15y - 4y = 0
-19y = 0
Dividing both sides by -19, we get:
y = 0
Now, we can substitute the value of y back into one of the original equations to find the value of x. Let's use equation 1:
x - 5(0) = 6
x = 6
So, the solution to the system of equations is x = 6 and y = 0.