Question

Use elimination to find the solution to the system of equations.

4x + y = 12
2x - 3y = 6

A. x = 3 y = 0
B. x = 0 y = 12
C. x = 7 y = -16
D. x = 27/2 y = 7

Answer 1

try multiplying the first equation by 3 (that means multiply every term on both sides of the = sign by 3)
what do you get ?

Answer 2

Here is what I have so far:

3(4x + y = 12)

12x +3y = 36
2x - 3x = 6
------------
14x = 42
--- ---
0 14
42/14 = 3
Y=3

Answer 3

pretty close. once you get
14x = 42

you divide both sides by 14 to get
\[ \frac{14x}{14} = \frac{42}{14} \]
14/14 on the left is 1 and 1*x is just x so you get
x= 42/14
x= 3

so it is x=3 (not y)

can you find y using
4x + y = 12 (and x=3) ?

Answer 4

AH! Okay! Thank you!! That is where I messed up!

4x + y = 12

When x =3...

12x + y = 12

12/12 = 0 12/12 = 0
Y = 0

Answer 5

Your algebra looks wrong. you start with
4x + y = 12

When x =3...

x=3 means we replace any x we see in the equation with 3. Look for x, erase it, put in a 3 instead:

4*3 + y= 12 (4x means 4*x, and with x=3, 4x means 4*3)

4*3 is 12, so this is
12+y= 12

can you "solve for y" ? (I would add -12 to both sides)

Answer 6

OH!! So...

12+y=12
And then add -12?

12 + (-12) = 0

Now Y=0 :)

Answer 7

closer. you add -12 to both sides like this
12+y=12
12-12 + y= 12-12 (notice we still have y. it does not go away)

now simplify: 12-12 is 0 so we get
0 + y= 0

and 0+y is y (adding zero to y does nothing)
you get
y= 0

Answer 8

AH! Okay, I thought you meant actually add -12!

Thanks so much for your help!!!

Answer 9

I did mean add -12, but to both sides
so you should show the work for adding -12 to both sides

if you have time, watch this video and the few after to really get the knack of this
http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/v/simple-equations

Answer 10

Will do.. Thanks again. (: