Question

What is a possible first step in eliminating a variable in the following system of equations?

x + 7y = –15
2x + 7y = –9

a. Multiply the first equation by –1.
b. Multiply the second equation by –1
c. Multiply the first equation by –2.
d. All of the above

Answer 1

Is it multiply the first equation by -2?

Answer 2

The idea is that if you multiply an equation by a number, you can make one of the variables cancel after adding the two equations.

multiply by -1 means write -1* in front of every term

so a) multiply 1st equation by -1 means

-1*x + -1*7y = -1*–15
which simplifies to
-x -7y = 15
now add the 2nd equation

-x -7y = 15
2x + 7y = –9
2x-x -7y+7y = 15-9
notice the -7y + 7y cancels.

so that is a good step.

Answer 3

oooh, i thought with -2 it would have canceled out as well.

Answer 4

However, multiplying the 2nd equation by -1 is also a good step.

and if you multiply the 1st equation by -2
you will get a -2x in the first equation, which will cancel +2x in the 2nd

so they all look good...

Answer 5

oh so all of the above.