How is the multiplication or division property of equality used in the elimination method? Are the properties always needed? Explain.

Answer 1

Fractions are changed by dividing: 1/2=.5; 3/4=.75etc. You want to use the same function type through-out the problem.

To change a decimal to a fraction: 5/8=.625=625/1000

=125/200=25/40=5/8.

Answer 2

Yes! The properties just mean you’re “undoing” something... like dividing both sides by a number is technically division property and multiplying something to both sides is multiplication property.

once you eliminate a variable it should become a regular equation like ax+b=c ... so it becomes a regular one variable equation where you can use any of the properties!

Answer 3

If you multiply or divide both sides of an equation by the same number, the sides remain equal. Let's use a simple example.

2 + 3 = 5

6(2 + 3) = 5

12 + 18 = 5

28 = 5

23 = 0

Well, duh, I didn't multiply BOTH sides by 6.

6(2 + 3) = 5(3)

12 + 18 = 30

30 = 30

0 = 0

There we go.

When we solve a system of equations using elimination, we need to have one of the variables have opposite coefficients that will then cancel out. We often need to multiply one or both of the equations by a number to make this happen.

3x + 4y = 6

2x - 4y = 4

Here, 4y + (-4y) = 0, so we don't have to multiply anything.

3x + 4y = 6

x + y = 4

Now, neither has opposite coefficients. We can multiply the bottom equation by -3 to get the x's to cancel out or -4 to get the y's to cancel out. I'll do -3.

3x + 4y = 6

-3x - 3y = -12

Now, 3x + (-3x) = 0, so there we go.

Hope this helps!