Question

Select the correct choices that belong in the blank for the system of equations shown below.

24x - 39 = 165

-6x +13y = -51

In order to solve this system by elimination, Stacy ____________ by ______. Then, when she adds the equations together, the x terms will cancel.

A. multiplies the second equation; 4

B. multiplies the second equation; -4

C. multiplies the first equation; 4

D. multiplies the first equation; -4

Answer 1

@Vocaloid

Answer 2

For systems of equations you want to get rid of one variable, lets get rid of x
You would need 24x and -6x to both be either \(+24, -24\). Since we use addition to get rid of a variable we need -6x to remain negative.

How would you get -6x to be -24x?

Answer 3

The coefficients of the terms must be opposites, so they will have a sum of 0.

Answer 4

If you want a pair of terms to cancel when you add two equations together, what must be true about the coefficients of those terms?

Answer 5

The opposite of 24 is −24.

Answer 6

Right, so
\(-6\cdot x=-24?\)

Answer 7

x = 4

Answer 8

We can remove B and D, since we are multiplying -6 by 4
We must also multiply everything else in that equation by 4, which is the second equation

Answer 9

A. multiplies the second equation; 4

Answer 10

Yep

Answer 11

THANKS A LOT MAN

Answer 12

Sure :)