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) =

Algebra ->  Inequalities -> 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) =      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++6%5Cx+%2B+7%5Cy+=+-9%2C%0D%0A++++2%5Cx+%2B+5%5Cy+=+5+%29%0D%0A++We'll use substitution. After moving 7*y to the right, we get:
6%2Ax+=+-9+-+7%2Ay, or x+=+-9%2F6+-+7%2Ay%2F6. Substitute that
into another equation:
2%2A%28-9%2F6+-+7%2Ay%2F6%29+%2B+5%5Cy+=+5 and simplify: So, we know that y=3. Since x+=+-9%2F6+-+7%2Ay%2F6, x=-5.

Answer: system%28+x=-5%2C+y=3+%29.



or
(x, y) =(-5, 3)

Answer by Alan3354(69443) About Me  (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(52784) About Me  (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  = -24%2F%28-8%29 = 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 = -10%2F2 = -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.

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

Less computing - less chance to make an error.