Question

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.​

Answer 1

1) x=0, y=3

2) no solutions

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