SOLUTION: I am trying to help my son without a textbook because his school does not supply textbooks. We have been trying to find out how to use the elimination method for this problem. Plea

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Question 839308: I am trying to help my son without a textbook because his school does not supply textbooks. We have been trying to find out how to use the elimination method for this problem. Please help.
7x+y=-17
3x-10y=24
If you can show us step by step, we will surely appreciate any help and referrals. This is Algebra II. Thanks! Marnie M. Melton
Found 2 solutions by ewatrrr, josgarithmetic:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

Good! You found Algebra.com ... a number of 'excellent' tutors monitor the site.

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(39617) About Me  (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...
7x%2By=-17%2C
7x%2A10%2By%2A10=-17%2A10
70x%2B10y=-170
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Now your equivalent system is this:
---------------------------
70x+10y=-170
--------------------------
3x-10y=24
--------------------------
ADD the two equations, member for member:
%2870x%2B10y%29%2B%283x-10y%29=-170%2B24
73x%2B10y-10y=-146
73x%2B0=-146
x=-146%2F73
highlight%28x=-2%29
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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.