SOLUTION: 5x - 5y = 10 3x - 2y = 2 Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 5x - 5y = 10 3x - 2y = 2 Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to      Log On


   

Question 879542: 5x - 5y = 10
3x - 2y = 2
Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this.
Part B: Show that the equivalent system has the same solution as the original system of equations.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Your part A and part B are a little difficult to follow but maybe this will help:

5x-5y=10 can be simplified, dividing left and right members by 5, to give x-y=2.

Your system is then equivalent to
x-y=2 and 3x-2y=2.
You can solve this system with the Elimination Method. The simplest way to start this is to try to match the coefficient on y in the second equation of the system. The way to do this is multiply the left and right members of the first equation by 2, yielding the system: 2x-2y=4 AND 3x-2y=2.
Now, simply subtract one equation from the other equation:
2x-2y-%283x-2y%29=4-2
2x-2y-3x%2B2y=2
-x%2B0=2
highlight%28x=-2%29
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Now, you might prefer not to again use elimination of x in order to find y; but instead to simply substitute for x=-2 in either equation of the system and solve for y.


... y=-4.