Hi

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Thank You for Your kind words.

using the elimination method:

7x+y=-17    |Multiply 1st EQ by 10 and add to 2nd to eliminate y

3x-10y=24 



70x+10y=-170    |Multiply 1st EQ by 10 and add to 2nd to eliminate y

 3x-10y=24

  73x = -146

    x =  -2   and y = -3  |Note: 7x+y = -17, -14 + y = -17,  y = -3

CHECKING our answer***

using: 3x-10y=24 

  -6 + 30 = 24 

Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
 FIND a used textbook!  Plenty of GOOD but old textbooks are easily found at library booksales.





If you have ANY equation and another equation, such as

ax+by=c  and k=j, then you can do like this:

ax+by+k=c+k;

knowing that k=j from the second equation means that, 

ax+by+k=c+j because you use that second equation to substitute for k.  Equality is maintained.

-

Also, you can multiply left and right members of an equation by a contstant, and the result is an equivalent equation, like k=j is the same as k*h=j*h.  This should make sense intuitively





You want to eliminate one of the variables in your given system of equations and then solve for the other variable.  You do this by multiplying one or both equations by constants so that you get an equivalent SYSTEM of equations with both coefficients on one variable being the same.





Easiest choice for your given system is multiply the "-17" equation by 10...







-

Now your equivalent system is this:

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

70x+10y=-170

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

3x-10y=24

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

ADD the two equations, member for member:











-

Now go back and solve for y; you should usually not need to produce an elimination to do this because you have the x value already and are able to choose either equation, substitute for x, and simply solve for y. 

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