Can you help with me my math h/w please?

Question

Can anyone explain to me how you do the elimination method to solve a system of equations. For example:
-3x+y=-4
2x-y=1

Answer 1

Since you have a +y and a-y you can eliminate them by adding the like terms of the two equations. -3x + 2x = -x. The y's are eliminated. -4 + 1 = -3. What remains is -x = -3. Multiply both side by -1 and x = 3. Substitute 3 for x in either equation and
y = 5.

Suppose the equations had been: -3x +y = -4
2x - 2y=-4

By multiplying every term in the first equation by 2 you would have: -6x + 2y = -8
2x - 2y = -4

Now the +2y and -2y can be eliminated. Adding like terms you are left with: -4x = -12, then x = 3. Substitute again and y = 5.

The second example is what you have to do in order to get like terms that can be eliminated. When you do the multiplying you have to multiply every term in the equation by the same number.

Sometimes it may be necessary to multiply both equations, each by a different number. For examlple,

2x + 4y = 14
3x - 3y = 3

If you multiply the first equation by 3 and the second by 4 you have: 6x + 12y = 42
12x - 12y = 12

Then 18x = 54, after eliminating the y's. Then x = 3, y = 2.

Answer 2

I'm not familiar with the term 'elimination method' but here's what I'd do.

First add the 2 equations together. You get -x = -3, so x=3. Then substitute 3 for x in either equation, and solve for y. Using the second equation, it's:
2(3)-y=1
6-y=1
-y=-5
y=5

Then go back and substitute 5 for y, and 3 for x, in both equations separately, and see if that works. If so, you know you have the right answer.

Answer 3

don't u add or subtract one from the other to eliminate a variable?

-3x + y = -4
+2x - y = 1
____________
-x +0y = -3

-x = -3

x = 3

now plug it into the top equation:

-3(3) + y = -4
-9 + y = -4
y = 5

x =3, y =5

plug them into the 2nd equation to check:

2(3) - 5 = 1

6 - 5 = 1

1 =1

check!