I just need a little help remembering can somebody please help me?

Question

1. Solve by substitution or elimination method:

3x - 2y = 8

-12x + 8y = 32

2. Solve by substitution or elimination method:

7x - 5y = 14

-4x + y = 27

3. Solve by substitution or elimination method:

-4x + 3y = 5

12x - 9y = -15

Answer 1

1) 3x=2y+8

x=2/3y+8/3

-12(2/3y+8/3)+8y=32

-8y+-32=32

-8y+0

y=0

just do the same for the other 2.

solve for one variable and plug it in in the other equation

Answer 2

1. Solve by substitution or elimination method:

3x - 2y = 8

-12x + 8y = 32

Multiply the first equation by 4 and add the equations together (elimination method).

12x - 8y = 32

-12x + 8y = 32

------------------------------

0x + 0y = 64

0 = 64

Since you have a contradiction, there is no solution...

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2. Solve by substitution or elimination method:

7x - 5y = 14

-4x + y = 27

Solve the second equation for y by adding 4x to each side...

y = 27 + 4x

Substitute this value into the other equation (substitution method)...

7x - 5(27 + 4x) = 14

7x - 135 - 20x = 14

-13x = 149

x = -149/13

Plug this back into the second equation...

-4(-149/13) + y = 27

596/13 + y = 27

y = 27 - 596/13

y = 351/13 - 596/13

y = -245/13

Plug these values back into each equation to check...

7(-149/13) - 5(-245/13) = 14

-1043/13 +1225/13 = 14

-1043 +1225 = 182

182 = 182 CHECK

-4(-149/13) + (-245/13) = 27

596/13 - 245/13 = 27

596 - 245 = 351

351 = 351 CHECK

Your answer is

x = -149/13

y = -245/13

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3. Solve by substitution or elimination method:

-4x + 3y = 5

12x - 9y = -15

Multiply the first equation by 3 and add the equations (elimination method)

-12x + 9y = 15

12x - 9y = -15

0x + 0y = 0

0 = 0

These equations are equivilant.  All values that satisfy the first equation satisfy the second.