3x + 8y = 12 2x + 2y = 3 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. (6 points) part b: show that the equivalent system has the same solution as the original system of equations. (4 points)

Ok here is what I think.
Let us first number these statements, as #1, and #2.
First statement: 3x + 8y = 12 (1)
Second Statement: 2x + 2y = 3 (2)
Now, we can work from this.
We want to make one of the equations be equal to 0 so that at the end when we check they can be equal to each other.
Let us use 4.
3x+8y=12      1-8x-8y=-12    2
This gives us:-5x = 0          
Now we should try and isolate x so we can substitute it into one of the equations.
We have -5x=0
and x=0
3(0)+8y=12
8y=12
y=12/8
y=3/2
Plug in these new equations
y=3/2 and y=0 into any of the first equations
 3x+8y=12                3(0)+8(3/2)= 12       8(3/2)=12                 4(3)=12                    12=12                           
Now we know it works, thats our check^^

What are you asking ?