algebra 1 answer please urgent!

Question

A system of equations is shown below:

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)

Answer 1

3x+8y =12    eqn 1

2x+2y=3       eqn 2

 

Let's multiply eqn 2 by -4 in order to create an equation

where the y variables will add to 0 when we sum the 

new equation 2 with the original equation 1

 

3x+8y=12       eqn 1

-8x-8y=-12    4(eqn 2)

--------------

-5x = 0          new eqn

 

We now have one original equation and the sum of that equation with a multiple of the other...

 

3x+8y=12

-5x=0

 

B.  3x + 8y=12  eqn 1

      -5x = 0        eqn 2

 

in eqn 2 solve for x

-5x=0

x= 0

insert 0 in place of x in eqn 1...  3x+8y=12

3(0)+ 8y= 12

8y=12

y = 12/8 = 3/2

 

Our solution is x=0    y = 3/2

 

To show that this is the same solution as the original set of equations 

we can plug the answer into the original equations to show that it is correct.

 

1.    3x+8y=12                2.  2x+2y=3

       3(0)+8(3/2)= 12.          2(0)+2(3/2)=3

        8(3/2)=12.                   2(3/2)=3

        4(3)=12                       1(3)=3 

        12=12                            3=3

       this works                       This works

 

As can be seen, the solution (0, 3/2) is correct

for both sets of equations.