SOLUTION: Solve the systems of equations by using the substitution method. (If the system is dependent, enter a general solution in terms of c {6x+ 7y = −9 2x+ 5y =5 (x, y) =

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Question 1131011: Solve the systems of equations by using the substitution method. (If the system is dependent, enter a general solution in terms of c
{6x+ 7y = −9
2x+ 5y =5
(x, y) =
Found 3 solutions by MathLover1, Alan3354, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 7*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: So, we know that y=3. Since , x=-5.

Answer: .



or
(, ) =(, )
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
It might be possible to get all the answers, and never learn how to solve the problems.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

Let me show to you  much  MORE  REASONABLE  way  to solve it by the Substitution method. 

6x + 7y = -9      (1)
2x + 5y =  5      (2)


The term " 6x " in equation (1) is three times the term "2x" in the in equation (2).

Therefore, it is TOTALLY ENOUGH to express 2x from equation (2) as  2x = 5 - 5y  and then substitute it into 
equation (1), replacing " 6x " there  as 3*(2x). You will get then


    3*(5-5y) + 7y = -9

    15 - 15y + 7y = -9

    -8y = -9 - 15 = -24

    y  =  = 3.


Now substitute this value  y= 3 into equation (2) to get

    2*x + 5*3 = 5

    2x + 15 = 5

    2x = 5 - 15 = -10

    x =  = -5.


Answer.  The solution is  x= -5,  y= 3.


Check the solution on your own by substituting the found values into the given equations.

Solved.

---------------

By doing in this way, you avoid working with fractions and denominators.

Less computing - less chance to make an error.



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