SOLUTION: how do you solve the system of equations using substitution? 3y=-7x+10 3y=4x+38

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Question 1132726: how do you solve the system of equations using substitution?
3y=-7x+10
3y=4x+38
Found 3 solutions by MathLover1, Alan3354, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

...eq.1
....eq.2
_____________________________
start with
...eq.1...solve for
-> substitute in eq.2

....eq.2






go back to -> substitute





solutions: and


Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
how do you solve the system of equations using substitution?
3y=-7x+10
3y=4x+38
------------
Sub for 3y in the 2nd eqn.
---
3y=4x+38
-7x+10 = 4x+38
11x = -28
x = -28/11
=============
3y=4x+38
3y = -112/11+38 = -112/11 + 418/11
3y = 306/11
y = 102/11
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

            It can be done in much simpler way,  and you deserve to know it . . . 


From the first equation, you just have the expression for 3y: it is -7x + 10.


Substitute it into the second equation in whole, as is, replacing 3y in its left side by -7x + 10.


You will get


   -7x + 10 = 4x + 38.   (*)


It is how the substitution method works in this case (or, it is the way on how YOU CAN USE the substitution method in this case).


So, you MOMENTARILY obtain a single equation for one unknown x, which you easily can solve.  From (*), you have


    10 - 38 = 4x + 7x

    -28 = 11x  ====>  x = .


As the next and last step, you substitute the found value of x into either of the two given equations to determine y.


    3y =  =  =   ====>  y =  = .


ANSWER.  x = ,  y = .

Solved   //   by using the substitution method   //   in its economic mode.

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

For other similar solved problems,  see the lesson
    - Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method
in this site.


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