Stacy was given the two equations 3x + 2y = 6 and y = x+3. "I've checked and checked my solution, but I keep getting 0 = 0. I don't know what I did
wrong.
"Oh, that's nothing" chimes in Eulalia. "My equations are 5x - y = 10 and -10x + 2y = -30, but I keep getting 0 = 10, which isn't even true.

explain to these two students what must be going on with their problems.

1) x=0, y=3

2) no solutions

Step-by-step explanation:

1) solve the first system of equations with elimination:

3x+2y=6

bring "y" to the right and "3" to the left

-3=x-y

x-y=-3

multiply with 3 so you can eliminate the variables:

3(x-y)=-3(3)

3x-3y=-9

-

3x+2y=6

      -5y=-15

         y=3

lets solve the equation for "x"

3x+2(3)=6

3x+6=6

2) 5x-y=10

-10x+2y=-30

a) make a variable in the first equation cross out with a variable in the second

2(5x-y)=(10)2

10x-2y=20

-10x+2y=-30

0=-10

this is a false solution, hence its no solutions

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