i need some homework help please?

Question

1. 2x-2y=2
x+2y=10

2. 4x+y=-11
3x-y=-10

3. 4x+3y=-23
3x-3y=-12

i am solving systems of equations by SUBSTITUTION.

Answer 1

1.2x-2y=2....(eqn 1)
x+2y=10
or,x=10-2y....(eqn 2)
Plugging x in eqn 1
2(10-2y)-2y=2
=>20-4y-2y=2
=>-6y=2-20= -18
=>y= -18/-6=3
Plugging y in in eqn 2
x=10-2*3=10-6=4
2)4x+y= -11
or y= -11-4x.......(eqn 1)
3x-y= -10
=>3x-(-11-4x)= -10
=>3x+11+4x= -10
=>7x= -10-11= -21
x= -21/7= -3
Plugging x in eqn 1
y= -11-4*-3= -11+12=1
3)4x+3y= -23.....(eqn 1)
3x-3y= -12
=>3x= -12+3y
=>x=(-12+3y)/3=-4+y.....(eqn 2)
Plugging x in eqn 1,we get
4(-4+y)+3y = -23
=>-16+4y+3y= -23
=>7y= -23+16= -7
=>y= -7/7= -1
Pkuggin y in eqn 2
x= -4-1= -5

Answer 2

2x-2y=2
x+2y=10

Solve the second equation for x and substitute into the first equation

x = 10 - 2y

2(10 - 2y) - 2y = 2
20 - 4y - 2y = 2
- 6y = - 18
y = 3

x = 10 - 2(3)
x = 10 - 6
x = 4

check

2x - 2y = 2
2(4) - 2(3) = 2
8 - 6 = 2
2 = 2

Note that these equations are ready to be solved by addition - add the two equations together

2x-2y=2
x+2y=10
- - - - - - -
3x = 12
x = 4

x + 2y = 10
4 + 2y = 10
2y = 6
y = 3

In fact, your problem 3 is best solved by addition

4x+3y=-23
3x-3y=-12
- - - - - - - -
7x = - 35
x = - 5

4x + 3y = - 23
4(-5) + 3y = - 23
-20 + 3y = - 23
3y = - 3
y = -1

check

3x - 3y = - 12
3(-5) - 3(-1) = - 12
- 15 + 3 = - 12
- 12 = - 12

Answer 3

2x - 2y =2- - - - - -equation 1
x +2y = 10- - -- - -equation 2
- - - - - - - - -
3x = 12

divide both sides of the equatio by 3

3x / 3 = 12 / 3

x = 12 / 3

x = 4

Insert the x value into equation 1
- - - - - - - - - - - -

2x - 2y = 2

2(4) - 2y = 2

8 - 2y = 2

Transpose 8

3 - 2y - 8 = 2 - 8

- 2y = - 6

Divide both sides of the equation by - 2

- 2y / - 2 = - 6 / - 2

y = 6/2

y = 3

Insert the y value into equation 1
- - - - - - - - - - -

Check for equation 1

2x - 2y = 2

2(4) - 2(3) = 2

8 - 6 = 2

2 = 2

- - - - - - -

Check for equation 2

x + 2y = 10

4 + 2(3) = 10

4 + 6 = 10

10 = 10

- - - - - - - - -

Both equations balance

The solution set is { 4, 3 }

- - - - - - - - -s-

Answer 4

1. Pick one of the equations and set it equal to either x or y
2x-2y=2
x=10-2y

2. Now substitute what x is equal to into the other equation
2(10-2y) - 2y=2

3. Solve
20-4y-2y=2
20-6y=2--> -6y=-18
y=3

4.Now that you have what y is equal to plug it back into one of the original equations to find what x equals

x+2(3)=10--> x+6=10
x=4
Your answer should be written as (4,3)

Problem 2. y=-11-4x
3x-y=-10

3x-(-11-4x)=-10
3x+11+4x=-10
7x=-21
x=-3

3(-3)-y=-10
-9-y=-10
-y=-1
y=1

Answer: (-3,1)

problem 3.
problem 3 will be easier to solve by addition

4x+3y=-23
3x-3y=-12

the positive and negative 3y will cancel each other out so you get...

7x=-35
x=-5
4(-5)+3y=-23
-20+3y=-23
3y=-3
y=-1

Answer: (-5,-1)

Hope this helped!

Answer 5

SO SUBSTITUTE!!!

2x - 2y = 2
x + 2y = 10 ==>> x = 10 - 2y OMG I GOT x!

2(10 - 2y ) - 2y = 2 !!!! wtf i put 10 - 2y where x was!

20 - 4y - 2y = 2
6y = 18
y = 3

DO THE REST MANG ITS NOT THAT HARD!