SOLUTION: -3x+7y=-16 -9x+5y+16 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

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: -3x+7y=-16 -9x+5y+16 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       Log On


   

Question 939459: -3x+7y=-16
-9x+5y+16
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.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Part A: Two ways to do this.
Eliminate y this way...

system%28%28-5%29%28-3x%2B7y%29=-5%28-16%29%2C7%28-9x%2B5y%29=7%2A16%29

system%2815x-35y=80%2C-63x%2B35y=168%29

Now just sum the left members, sum the right members, set them equal.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

-3x+7y=-16
-9x+5y+16
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.


- 3x + 7y = - 16 -------- eq (i)

- 9x + 5y =   16 -------- eq (ii)

Is the 2nd plus sign in the 2nd equation supposed to be "="? If so, then the most convenient method is to:

1) Multiply eq (i) by - 3, creating eq (iii)

2) Sum eqs (iii) &  (ii), thus eliminating x

3) Determine the value of y.