Asked by Bella

Im studying for finals!

A system of equations is shown below:
8x + 5y = 9 3x + 2y = 4

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.
Answered by Reiny
A: let's add them as suggested:

11x + 7y = 13
multiply the 2nd by 2
6x + 4y = 8
Note: the system : 11x+7y = 13 and 6x + 4y = 8 is not unique, I could have done anything I wanted here.

B.

ok, let's solve the original system:
#1 times 2: 16x + 10y = 18
#2 times 5: 15x + 10y = 20
subtract them:
x = -2
back in the original #1
8(-2) + 5y = 9
5y = 25
y = 5

so x = -2, y = 5

test these in our new system of A
11x + 7y = 13
11(-2) + 7(5) = -22 + 35 = 13, Yeah!

6x + 4y = 8
6(-2) + 4(5) = -12 + 20 = 8, yeahhhhh!!!!
Answered by Bella
Okay so for part A I should put the answer is 6x + 4y = 8 ?
Answered by Reiny
No,
you want a "system", which means you need two equations.
My new system was:
11x + 7y = 13 and 6x + 4y = 8

The original 8x + 5y = 9 was replaced by the sum of the two original equations,
and the original 3x + 2y = 4 was replaced by a multiple of that (I multiplied it by 2)

I just followed their instructions.
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