Math methods, First answer gets 10points!?

Question

Please use the substitution method and show solution
4x + 3y = 0 ; 2x - y = 0
Please use the addition method and show solution
2x - 5y = -1 ; 3x + y = 7
First correct and showed solution will be choosen as best answer, ty all!!

Answer 1

1) Using the substitution method, the second equation is easy to solve for y to get y = 2x. Substitute this in to the first equation and you get 4x + 3(2x) = 0, which means 10x = 0 and thus x=0. Plugging this back into the second equation gives 2(0) - y = 0, -y = 0, so y=0. (This makes sense, since you can rewrite both equations in the form of y=mx, to get two lines both passing through the origin.)

2) To use the addition method, we see a -5y in the first equation and a +y in the second, so multiply the second by 5 and add it to the first. You get
(2x-5y) + 5(3x+y) = -1 + 5(7)
2x - 5y + 15x + 5y = -1 + 35
2x + 15x= 34
17x= 34
x = 2. Plug this back in to either equation and solve for y:

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

Answer 2

1) Substitution method. First, substitute for y in the second equation. Makes it easier.

4x + 3y = 0

2x - y = 0
y = 2x

Now substitute y back into the first equation.

4x + 3y = 0
4x + 3(2x) = 0
4x + 6x = 0
10x = 0

i think you may have written this equation up incorrectly, since in this case both x and y = 0.


2) You add each side of the equations separately in this case. Multiply the second equation by 5 to eliminate y.

2x - 5y = -1
15x + 5y = 35
17x = 34
x = 2

Plug this back into the equation to get y.

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

x = 2
y = 1

Answer 3

Gee, try something tough.
To substitute, solve the second eqtn for 2x. Then double it. Then dump it in for 4x in the first. That will give you y. Then go back to either original eqtn to get x.

To use addition method, multiply eqtn 2 by 5 so you have a +5y terem in it. Then add that equation to the first equation. There will be no y left and you can solve for x. Then go back to solve either of the original eqtns for y.

Answer 4

1st answer: x=y=o
2nd answer: x=2, y=1