ok.......i have this algebra prob. i need help w/.?

Question

2x +5y =16,

4x-3x = -7.

The first prob is over the second one

its called the elimination method..and no this isnt homework.....i just cant figure it out.

Answer 1

4x - 3x = -7
x = -7

2x + 5y = 16
-14 +5y = 16
5y = 30
y = 6

Answer 2

For every unknown you are faced with, you need one equation. In this problem, you are faced with 2 unknowns, x and y. You need 2 equations. You have them. We're set to go.

There are 2 methods available for solving them.
One way is the SUBSTITUTION method. You use one equation to find x in terms of y, and substitute what you get for x in the unused equation. Here's an example:
From your system of equations I choose the first equation to find x in terms of y
2x + 5y = 16, 2x = 16- 5y, x = (16-5y)/2
I then substitute (16-5y)/2 for x in the unused equation to get
4[( 16-5y)/2] -3y = -7
2(16-5y)-3y =-7 ,32 -10y -3y = -7, -13y = -39, y=3

Knowing y, x is found simply by plugging in 3 for y in
either of the 2 original equations, like this:
4x -3y =-7, 4x-3(3) =-7, 4x -9= -7, 4x=2, x =1/2.

The other method for solving is the ELIMINATION method, which is what you asked about in the first place! Sorry to be so chatty about this- I just think you need the full story.
In the elimination method, we manipulate one or both equations so that one variable, when the equations are added together, just goes "poof" and disappears.
It gets eliminated. For your system of equations,
2x +5y = 16
4x - 3y =-7
I shall multiply the top equation by -2. I get
- 4x -10y = -32
4x - 3y = -7 remains untouched. I now add these two equations together to get
______________
-13y =-39, y=3
As before x is 1/2

What gave me the right to add these two equations together? Simple law of math, which says whatever you do to one side of the equation, do the same thing to the other side and it's legitimate. So that's what I did.
First I multiplied BOTH sides of 2x + 5y = 16 by -2
I deliberately picked -2 because that's what gave me
an x term equal in magnitude but opposite in sign to
the x term in the second equation. Now here's the key step: I added 4x - 3y from the second equation to the left side of the top equation, and the x terms eliminated each other, leaving only a y term. WAIT A MINUTE ! I hear you scream. "you should have added 4x - 3y to the right side too!" Well I did.
4x -3y = -7 so I added -7 instead of 4x -3y.

And that's the old Elimination method

Glad to be of help.
By the way, you wrote your second equation as
4x - 3x = -7. You meant 4x -3y =-7 didn't you? If you get funny answers or very few answers, that's probably why. If on the other hand you really did mean 4x -3x = -7, then forget everything I've written to you.

Cheers!

Answer 3

i think the best way would be to start wtih the second equation first: 4x-3x= -7 which would be 1x=-7

Then you can multiply 1x= -7 by 2,.... 2(1x= -7) so that will equal to: 2x= -14 then you can now substitute that 2x= -14 into the first equation which would be: -14 + 5y = 16
Then bring the -14 over to the 16 side which would be positive 30. Thus leaving you with 5y= 30

Then divide 30 by 5 so you can find out what Y would be.
Making Y=6

hope that helps...

Answer 4

1st equation:
2x + 5y = 16
2x = 16 - 5y
x = 8 - 2.5y

2nd equation:
4x - 3x = - 7
x = - 7

3rd equation:
8 - 2.5y = - 7
2.5y = 15
y = 6

Answer: x = - 7, y = 6

Proof:
2(- 7) + 5(6) = 16
-14 + 30 = 16
16 = 16

4(- 7) - 3(- 7) = - 7
- 28 + 21 = - 7
- 7 = - 7

Answer 5

The 2nd equ. Is not right
may be you mean
4x - 3y = -7
for this method try to get the coefficent of of one variable such (x) in one equation is equal and negative sing to the other in the other equation
multiply equ (1) by 2
4x +10y = 32
multiply equ. (2) by -1
-4x + 3y = 7
then we have got
4x +10y = 32 Equ (1)
-4x + 3y = 7 Equ (2)

by adding the two equ.
13y = 39
then y = 3
and then in equ (1)
4x +30 = 32
then
4x = 2
x = 0.5
then we get
x =0.5
y = 3

Answer 6

1)set the first equation = to y
2x+5y=16
5y=-2x+16
y=-2/5x + 8

2)solve the second
4x-3x=-7
x=-7

3) set x in the first to -7
y=-2/5(-7) + 8
y=14/5 + 8
y=10 4/5

Answer 7

I will assume that we have
2x+5y=16
4x-3y=-7

so, let´s see, what happens if we add them?we would get:
6x+2y=9
and then, what if we substract twice the first one from the second one:

4x-3y - (4x+10y)=-7-32 ---->-13y=-39, then y=3 and the value of x you´ll get it replacing on any equation.

Have a nice day!

Answer 8

4x-3x = -7.
so x=-7.
2(-7) +5y = 16
-14 + 5y = 16
5y = 30
y = 6

Answer 9

2x+5y=16
4x-3x=-7

2x+5y=16
1x=-7(divide)

2x+5y=16
x=-7

2(-7)+y=16substitute)

-14+y=16(get y by itself)
+14 +14

y=30

Answer 10

Are you sure you wrote that out correctly? Because you have two x terms in the second equation.

And, what are you solving for? An x and y (assuming the second equation has a typo) that is the solution for both equations?