Who can solve these problems?

Question

1) x - 3y = 6

-x + 3y = -3

2) 2y - 5x = 10

10x - 4y = 6

3) 2x + 3y = 7

x - 4y = -13

4) 3x + 2y = 8

2x - y = 3

these are the systems of equations I don't get...

Answer 1

1st problem:

x - 3y = 6

3y = x - 6

- x + 3y = - 3

3y = x - 3

Solve for x:

x - 6 = x - 3

0 = 3 is FALSE

Answer: There is no solution to this problem. The equation is FALSE.

2nd problem:

2y - 5x = 10

2y = 5x + 10

10x - 4y = 6

5x - 2y = 3

2y = 5x - 3

Solving for x:

5x + 10 = 5x - 3

0 = - 13 is FALSE

Answer: There is no solution to this problem.

3rd problem:

2x + 3y = 7

3y = 7 - 2x

y = (7 - 2x)/3

x - 4y = - 13

4y = x + 13

y = (x + 13)/4

Solving for x:

4(7 - 2x) = 3(x + 13)

28 - 8x = 3x + 39

11x = - 11

x = - 1

Solving for y:

= (7 - 2[- 1])/3

= (7 + 2)/3

= 9/3 or 3

Answer: x = - 1; y = 3

Proof (1st equation):

2(- 1) + 3(3) = 7

- 2 + 9 = 7

7 = 7

Proof (2nd equation):

- 1 - 4(3) = - 13

- 1 - 12 = - 13

- 13 = - 13

4th problem:

3x + 2y = 8

2y = 8 - 3x

y = (8 - 3x)/2

2x - y = 3

y = 2x - 3

Solving for x:

8 - 3x = 2(2x - 3)

8 - 3x = 4x - 6

7x = 14

x = 2

Solving for y:

= (8 - 3[2])/2

= (8 - 6)/2

= 2/2 or 1

Answer: x = 2, y = 1

Proof (1st equation):

3(2) + 2(1) = 8

6 + 2 = 8

8 = 8

Proof (2nd equation):

2(2) - (1) = 3

4 - 1 = 3

3 = 3

Answer 2

Well,

1 and 2 can't be solved.

3) y = 3

   x = -1

4) x=2

   y =1

How told solve?

Well, I'll show you 3)

2x + 3y = 7

x   -  4y = -13

You multiply -2 to the bottom equation..and you get,

2x +  3y = 7

-2x+  8y = 26

Now, you add both the equations, and you get..

          11y = 33

Therefore, y = 3

Since you have 3, you can go back to one of the original equation..

Like,  2x + 3y = 7   and plug the y-value into the y

So, you get  2x + 3(3) = 7

2x + 9 = 7

2x = 7 - 9

2x = -2

x = -1

Good luck!