Answer:
Nicole is correct, since when she multiplied by 3, she cleared the x's, since one x was already negative, and the other one was positive. Michael is incorrect since when he multiplied by 2, he didn't realize that both y's were positive, so they didn't clear.
Step-by-step explanation:
Let's see what will happen if we do what Nicole says:
x+2y=7
-3x+4y=9
multiply the first equation by 3 on both sides
3(x+2y)=7(3)
3x+6y=21
-3x+4y=9
now let's add them.
10y=30
We can see that the x's are cleared, since one x is positive and the other is negative.
Now let's try what Michael says.
x+2y=7
-3x+4y=9
multiply first equation by 2
2(x+2y)=7
2x+4y=7
-3x+4y=9
now let's add
-x+8y=16
the y's aren't eliminated, since both of them are positive.
Nicole is correct, since one x is positive and another was negative, and when opposite numbers are added together, they cancel out and equal zero.
Hope this helps!
