SOLUTION: solving linear systems using substitution, what is 4x-7y=10 y=x-7

Algebra ->  Systems-of-equations -> SOLUTION: solving linear systems using substitution, what is 4x-7y=10 y=x-7       Log On


   

Question 423206: solving linear systems using substitution, what is
4x-7y=10
y=x-7
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
4x-7y=10 .............1
x-y=7.............2

multiply (1)by -1
Multiply (2) by 7
-4x+7y=-10
7x-7y=49

Add the two equations

3x=39

/3

x=13

plug value of x in (1)

4x-7y=10
52-7y=10
-7y=10-52
-7y=-42
y=6

Answer by ikleyn(53419) About Me  (Show Source):
You can put this solution on YOUR website!
.
solving linear systems using substitution, what is
4x-7y=10
y=x-7
~~~~~~~~~~~~~~~~~~~~~~


        The solution in the post by @mananth is irrelevant, since it is done
        using the Elimination method, while the request was to use the Substitution method.

        I came to solve the problem as it is requested. 


Your starting equations are

    4x - 7y = 10    (1)
    y = x-7         (2)


Using equation (2), substitute y = x-7 in equation (1), replacing 'y' there

    4x - 7(x-7) = 10.


Simplify and find 'x'

    4x - 7x + 49 = 10

    49 - 10 = 7x - 4x

    39 =    3x

     x =     39/3 = 13.


Now from equation (2)  y = x - 7 = 13 - 7 = 6.


ANSWER.  x = 13,  y = 6.

Solved as requested.