Need help with math problem?

Question

Solve the system for x by the elimination method:

2x+2y=-5
x+2y=-2

It's either:

A: -3/2
B: -7/3
C: -3
D: 1/2

Also can you explain how you got it? Thanks.

Answer 1

C: -3

The elimination method has you take the two equations and manipulate them to eliminate the variable you do not need. Usually this will involve multiplying one of them by some convenient number and then adding/subtracting them (depending on that convenient number!). But, here they are already convenient (because both have 2y) so just subtract the 2nd equation from the 1st one:

(2x + 2y) - (x + 2y) = -5 - (-2) so:
2x - x + 2y -2y = -5 + 2 and:
x = -3


Added:

Everyone else is doing it by the substitution method or adding unneeded steps (why multiply by -1 and then add when you can simply subtract right away???). Or flat out getting it wrong by dropping signs, etc. That illustrates the need for keeping it as simple as you can! Less time wasted and far fewer mistakes to miss...

Answer 2

2x+2y=-5
x+2y=-2 subtract this equation from the 1 above
x=-3

C: -3 is corect
to find y, substitute -3 for x in either of the original equations
-3+2y=-2 add 3 to each side
2y=1 divide both sides by 2
y=1/2

check substitute -3 for x & 1/2 for y in the other equation
2(-3)+2(1/2)=-5
-6+1=-5
-5=-5

x=-3, y=1/2

Answer 3

The answer is C: -3.

This is how you solve using the elimination method:
Just like the name suggests, using the elimination method works by eliminating one of the variables. In this case, they want you to find x. You find x by eliminating all the other variables - in this case, y.

So the next step is to figure out how you can eliminate y. Since 2y - 2y = 0, you would subtract the equations from each other as such:

2x + 2y = -5
x + 2y = -2
----------------
x + 0 = -3 (2x - x = x, -5- -2 = -3)
x = -3.

Answer 4

The best method to solve this is elimination.

Multiply the 2nd equation by -1 to get rid of the y values(EVERYTHING)

2x+2y=-5
-x -2y= 2

Now add the x's, the y's, and the sums to each other. The y's will cancel out.

You get:
x=-3 which is C

Answer 5

It's D: 3.

The elimination problem is when you add the two equations together as if they were numbers, solving vertically. The setup equation would have to be

2x+2y=-5
+x+2y=-2

You must cancel the y's out if you want to solve for x, so you must find something that you can multiply one of the problems by. I would chose to muliply the bottom equation by -1, since it would cancel out the y's.

2x+2y=-5
-1(x+2y=-2)

then becomes

2x+2y=-5
-x-2y=2

Now, pretend it was one of those silly first grade problems and solve vertically.

2x - x = x
2y - 2y = 0 (they cancel out)
-5 + 2 = -3.

x = -3

Answer 6

C!

2x+2y=-5
-2(x+2y=-2)
-2y=-1
y=1/2


x+2(1/2)=-2
x+1=-2
x=-3

Answer 7

C!

2x+2y=-5
x+2y=-2

multiply the bottom one by -1 but both y are the same and we need to add them and have them cancel out

(-1) x + 2y = -2 becomes -x-2y=2

2x+2y=-5
-x-2y=2

now add it all up and you get

x = -3, (2x-x = x) (the y's cancel each other out) (-5+2 = -3)

Answer 8

Solve the 2nd equation for x. This gives you x=-2-2y.
The substitute that for the x in the first equation.
2(-2-2y)+2y=-5
-4-4y+2y=-5
-2y=-1
y=1/2

Answer 9

C. -3
Solve the second equation for x and you get x=-2-2y
Then sub that into the first equation and solve for y. YOu get 1/2. Put 1/2 in for y in either equation and you get x=-3

Answer 10

2x+2y=-5....(1)
x+2y= -2.....(2)
subtracting )2) from (1),we get
x=-3