Solving By a System of Equations (Algebra) HELP!!?

Question 1:
1. look closely you see you have 5y and -5y these cancel just by adding together giving you
7x=-21
x=-3
2. Now substitute -3 in for x and solve for y
-9 - 5y =11
-5y = 20
y = -4
Answer (-3,-4)
Check -9 +20 =11
11=11 (correct)

Question 2:
multiply the second equation by -3 to clear the x or -4 to clear the y
3x+4y=-9
-4x-4y=8
-x=-1
x=1
1+y=-2
y=-3
answer (1,-3)

0r solve the second equation for either x or y and substitute back into the fist equation
y=-2-x

3x+4(-2-x)=-9
3x-8-4x=-9
-x-8=-9
-x=-1
x=1
1+y=-2
y=-3
answer (1,-3)

4x + 5y = -32
3x - 5y = 11

Add them together.

7x = -21
x = -3

Plug this back in.

Use the first equation (this doesn't mean the second one doesn't work).

4(-3) + 5y = -32
-12 + 5y = -32
5y = -20
y = -4

(x,y) = (-3,-4)

Some teachers may want you to check this, but I won't bother.

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3x + 4y = -9
x + y = -2

Multiply the second equation by 3.

3x + 4y = -9
3x + 3y = -6

Subtract them

y = -3

Substitute back into the first equation (again, this doesn't mean the second equation doesn't work).

3x + 4(-3) = -9
3x - 12 = -9
3x = 3
x = 1

(x,y) = (1,-3)

Again, your teacher may want you to check this.

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EDIT:

Here's the general concept of solving these equations. Hope this can help you.

For solving simultaneous equations, we have to eliminate one of the variables and leave us with only ONE variable in an equation. The reason being that we cannot solve for a variable with an equation with two variables. So what we do is we add and subtract EQUATIONS to eliminate a variable. Sometimes you'll have to do some manipulation.

let x=# of baloons and allow y=# of streamers. the first equation would appear as if 7x+4y=26 and the 2d will be 3x+y=9. then you definately would set the 2d equation to a "y=..." style, which could be y=9-3x. Then plug this into the first equation: 7x+4(9-3x)=26 7x+36-12x=26 36-5x=26 -5x=-10 x=2 hence the balloons fee $2. Plug this x fee into the 2d equation (both one would paintings; the 2d one is basically the finest). y=9-3(2) y=9-6 y=3 hence the streamers fee $3 each and each and every. There you pass. :) Welp, a good type of others jumped on it already....

Questiion 1
7x = - 21
x = - 3

- 12 + 5y = - 32
5y = - 20
y = - 4

x = - 3 , y = - 4

Question 2
3(- 2 - y) + 4y = - 9
-6 - 3y + 4y = - 9
y = - 3

x = - 2 - y
x = - 2 + 3
x = 1

x = 1 , y = - 3

First problem:

You can add the equations together with the elimination method. Since you have a +5Y and a -5Y, they will cancel. Add (4X + 5Y) and (3X - 5Y) and you get (7X) since (5Y - 5Y = 0). Then you add -32 and 11 to get 21. you now have the equation 7X = 21. Divide by seven and you get X = 3. Plug X = 3 into 4X + 5Y = -32. 4(3) + 5Y = -32. Subtract 12 and divide by 5 to get Y = 8.8.

X = 3, Y = 8.8

You can add the equations like that because both sides of the equation are equal.

Problem 2:

You need to alter one of the equations so that two terms can cancel when you add them (like the first one). You can muiltiply the second equation -3. This leaves you with -3X - 3Y = 6. Now you can add the equations together to get Y = -3. The 3X and -3X cancel out. Now that you have Y, you can plug it in to find X. X + (-3) = -2. Add 3 to get X = 1.

X = 1, Y = -3

Use the elimination method!!!

1)
4x + 5y = -32 (solve by substitution)
3x - 5y = 11

4x + 5y = -32
5y = -32 - 4x

3x - 5y = 11
3x - (-32 - 4x) = 11
3x + 32 + 4x = 11
3x + 4x = 11 - 32
7x = -21
x = -21/7
x = -3

4x + 5y = -32
4(-3) + 5y = -32
-12 + 5y = -32
5y = -32 + 12
5y = -20
y = -20/5
y = -4

∴ x = -3 , y = -4

= = = = = = = =

2)
3x + 4y = -9 (solve by elimination)
x + y = -2

x + y = -2
3(x + y) = 3(-2)
3x + 3y = -6

...3x + 4y = -9
-- 3x + 3y = -6
---------------------
y = -3

3x + 4y = -9
3x + 4(-3) = -9
3x - 12 = -9
3x = -9 + 12
3x = 3
x = 3/3
x = 1

∴ x = 1 , y = -3

1) 4x+5y=-32
3x-5y=11
7x=21
x=21/7=3
2) 3x+4y=-9
x+y=-2 => 3x+4y=-9
3x+3y=-6 => y=-3
=>x-3=-2 => x=1

4x + 5y =-32 -----(1)
3x - 5y = 11 ------(2)
(1)+(2)
therefore,
7x = - 21
x = -3 put to (2)
therefore 3(-3) - 5y = 11
-9 - 5y = 11
-5y = 20
y = -4

1. Add them up, and you can see that the y term = 0

4x + 5y = -32
3x - 5y = 11 ---> add them, 7x = -21; x = -3

Plug int the original ewuation (either) to get Y

4(-3) + 5y = -32
-12 + 5y = -32
y = -4

7x=-21
x= -3

then

-9-5y=11
5y=20
y= -4
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another one


3x+4y=-9
x+y=-2 | *(-4)

it will be -4x -4y = 8

-x =-1
x=1

and for y:

3 + 4y = -9
4y = -12
y = -3