SOLUTION: need help with this problem. example with explanation, please. I want to understand the basics. 1. 6x - y = -9 x + 2y = 5

Algebra ->  Linear-equations -> SOLUTION: need help with this problem. example with explanation, please. I want to understand the basics. 1. 6x - y = -9 x + 2y = 5       Log On


   

Question 1095919: need help with this problem. example with explanation, please. I want to understand the basics.
1. 6x - y = -9
x + 2y = 5
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
There are several ways to solve this system.

Solution 1. Substitution method. 

6x -  y = -9,    (1)
 x + 2y =  5.    (2)


From equation (2), express x = 5-2y.  Then replace x in the equation (1) by (5-2y).

It is the substitution step. You will get a single equation in one unknown y:

6*(5-2y) - y = -9.


Simplify and solve for y:

30 - 12y - y = -9  ====>  30 + 9 = 12y + y  ====>  39 = 13y  ====>  y = 39%2F13 = 3.


Now substitute  y= 3 into equation (2). You will get

x + 2*3 = 5  ====>  x = 5 - 6 = -1.


Answer.  The solution is  x= -1,  y= 3.

For more examples and explanations, see the lesson
    - Solution of the linear system of two equations in two unknowns by the Substitution method
in this site.


Let me know if my responce was useful to you.
If you have questions, you can send them to me through the "Thank you" form.

If I see the interest from your side, I will write you more about different methods of solution to this system,
and will refer more lessons in this site to you.



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Equivalent system, system%2812x-2y=-18%2Cx%2B2y=5%29

%2812x-2y%29%2B%28x%2B2y%29=-18%2B5
12x%2Bx-2y%2B2y=-13
13x=-13
x=-1
and you should be able to do the rest.