Elimination Equations Algebra

I have the answers But i just needed to know how to get it by steps like show work? plus its not homework its just work that my teacher gave me but she wouldnt show me how it was misunderstanding actually


36. x = 2y + 3
3x + 4y = -1

37. 2y - x = -5
4y - 3x = -1

the answer is (-9, 7)

Substitution Method:
Since x = 2y + 3, we can substitute x with 2y + 3 in the equation 2,
x = 2y + 3
3x + 4y = -1

x = 2y + 3
3(2y + 3) + 4y = -1

Now calculate for the 2nd equation:
3(2y + 3) + 4y = -1
6y + 9 + 4y = -1

10y = -10
y = -1

Substitute "y" with -1:
x = 2y + 3
x = -2 + 3
x = 1

Answer: x = 1, y = -1

Another Method: Seperate the variables from the non - variables
x = 2y + 3
3x + 4y = -1

x - 2y = 3
3x + 4y = -1

Now that we got our equation, multiply both equation 1 by 2 in order to eliminate y:
x - 2y = 3

2x - 4y = 6
3x + 4y = -1

Add both equation:
2x - 4y = 6
3x + 4y = -1

5x = 5
x = 1

Substitute "x" with 1:
1 = 2y + 3
2y = -2
y = -1

Answer: x = 1, y = -1
_________________________

2y - x = -5
4y - 3x = -1

Substitution Method: Solve for "x"
-x = -5 - 2y
x = 5 + 2y

Now calculate for the 2nd equation:
4y - 3(5 + 2y) = -1
4y - 15 - 6y = -1
-2y = 14
y = -7

Substitute "y" with -7:
-28 - 3x = -1
-3x = 27
x = -9

Answer: x = -9, y = -7

Another Method: Multiply the equation by equation 1 by 2 to eliminate y
4y - 2x = -10
4y - 3x = -1

Subtract both equations:
4y - 2x = -10
4y - 3x = -1

x = -9

Substitute "x" with -9
4y - 3x = -1
4y + 27 = -1
4y = -28
y = -7

Answer: x = -9, y = -7

36.
6y + 9 + 4y = - 1
10y = - 10
y = - 1

x = - 2 + 3
x = 1

x = 1 , y = - 1

37.
- 4y + 2x = 10
4y - 3x = - 1----ADD

- x = 9
x = - 9

2y + 9 = - 5
2y = - 14
y = - 7

x = - 9 , y = - 7