SOLUTION: Solve the following system of equations: x-5y=20 2x+y=14 Please show me how you solve the problem, thanks.

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Question 1130523: Solve the following system of equations:
x-5y=20
2x+y=14
Please show me how you solve the problem, thanks.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Which or what method are you expected to use?

How about starting like this:
2%285y%2B20%29%2By=14

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Reading your post, I assume that you are a novice in this area.

So, I will show you the simplest method and the simplest way students usually learn this subject.


 x - 5y = 20     (1)
2x +  y = 14     (2)


From equation (1), express  x = 20 + 5y.   Then substitute this expression into equation (2), replacing x.

You will get a single equation for "y"


2*(20+5y) + y = 14


40 + 10y + y = 14

11y = 14 - 40

11y = - 26

y = -26%2F11 = -25%2F11.


Now substitute this value of y into equation (2) to get


2x + %28-26%2F11%29 = 14  ====>

2x = 14 + 26%2F11 = %2814%2A11+%2B+26%29%2F11 = 180%2F11 =====>  x = 90%2F11 = 82%2F11.


Answer.  x = 90%2F11 = 82%2F11;  y = -26%2F11 = -24%2F11.

After completing the solution,  check on your own that the answer is valid.
For it,  substitute the found values of x and y into the original equations.

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The method I used in the solution,  is called the Substitution method.

See the lesson
    - Solution of the linear system of two equations in two unknowns by the Substitution method
in this site.