Algebra Solving Linear Equations help?

Question

Please use the linear combination method or substitution method (would appreciate if linear combination i am having more troubles with that) to solve these problems i couldn't figure it out.. please and show a few steps of work i would greatly appreciate it. (Each comma seperates the 2 equations)

1) 2x-5y = 10 , -3x + 4y = -15

Answer 1

2x-5y = 10
-3x + 4y = -15 Multiply the 1'st equation by 3 and the 2'nd by 2

6x - 15y = 30
-6x + 8y = -30 Add them together
0x + 7y = 0 so y = 0. Now substitute 0 for y in the 1'st 2 equations to get x = 5.

Doug

Answer 2

3 x (2x - 5y = 10)
2 x (-3x+ 4y = -15)

6x - 15y = 30
add -6x + 8y =-30
--------------------
0 + 7y = 0
y = 0

substitute the result to the first equation,

2x - 5 x 0 = 10
2x = 10
x = 5.

Answer 3

2x - 5y = 10
5y = 2x - 10
y = (2x - 10) / 5

- 3x + 4y = - 15
4y = 3x - 15
y = (3x - 15) / 4

4(2x - 10) = 5(3x - 15)
8x - 40 = 15x - 75
7x = 35
x = 5

y = (2[5] - 10) / 5
y = (10 - 10) / 5
y = 0

Answer: x = 5, y = 0

Proof 1:
2(5) - 5(0) = 10
10 - 0 = 10

Proof 2:
- 3(5) - 4(0) = - 15
- 15 - 0 = - 15