Question

solve the system by using elimination or elimination with multiplication: 3x - 2y = 9 and -3x + 2y = -9.

Answer 1

3x - 2y = 9
-3x + 2 = -9

is there a y next to the 2 on the second equation?

Answer 2

yes, sorry it should be 3x - 2y = 9 and -3x + 2y = -9. thank you

Answer 3

if it is like this:

3x - 2y = 9
-3x + 2y = -9

then


In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 3 and -3 to some equal number, we could try to get them to the LCM.

Since the LCM of 3 and -3 is -3, we need to multiply both sides of the top equation by -1 and multiply both sides of the bottom equation by -1 like this:

-1(3x - 2y) = 9 * -1
Multiply the top equation (both sides) by -1

-1(-3x + 2y) = -9 * -1
Multiply the bottom equation (both sides) by -1


So after multiplying we get this:
-3x + 2y = -9
3x - 2y = 9

Notice how -3 and 3 add to zero, 2 and -2 add to zero, -9 and 9 and to zero. So in essence, they cancel each other out.


So we're left with

0=0


which means any x or y value will satisfy the system of equations. So there are an infinite number of solutions.


So this system is dependent.

Answer 4

Do you get this?

Answer 5

yes, thank you so much.