Help solve, not sure how to

2x-y-z=7
3x+5y+z=-10
4x-3y+2z=4

add the first two equations together to eliminate the z term
2x-y-z=7
3x+5y+z=-10
gives you
5x +4y = -3
double the first equation
4x -2y -2z = 14
and add it to the third equation to again eliminate the z term
8x -5y = 18

you have 2 equations 5x +4y = -3 and 8x -5y = 18
multiply 5x +4y = -3 by 5
25x + 20y = -15
and multiply 8x - 5y =18 by 4
32x - 20y = 72
add these together to eliminate the y term
57x = 57
x = 1
To solve for y take 5x +4y = -3 and substitute 1 for x
5(1) +4y = -3
4y = -8
y = -2
Now take one of the original equations and substitute 1 for x and -2 for y and solve for z
2(1) -(-2) -z = 7
4-z = 7
-z = 3
z = -3
So x =1, y = -2, and z = -3

(1) 2x - y - z = 7
(2) 3x + 5y + z = -10
(3) 4x - 3y + 2z = 4

After naming the equation, we will start combining the equation from here
(1) + (2) = 2x - y + 3x + 5y = -3
= 5x +3 +4y = 0 => We call this equation (N1)

(2)*2 - (3) = 6x + 10y - 4x + 3y = - 24
= 2x + 13y + 24 = 0 <=> 2.5*(2x + 13y + 24) = 0 <=> 5x + 32.5y + 60 = 0
We call this equation (N2)

Take N2 - N1, we have
32.5y + 60 - 3 - 4y = 0
=> 28.5y = - 57
=> y = - 2

Putting y = - 2 in N1 , we can find x
(N1) 5x + 3 - 8 = 0 => 5x = 5 => x = 1

Putting x = 1; y = - 2 in (1), then we can find z

2*1 - (-2) - z = 7
=> 4 - z = 7 => z = - 3

The answer for the system of equation will be

(x; y; z) = (1; -2; -3)

If you are happy with my explanation, please give it 10 points. Thank you very much

2x - y - z = 7.....(1)

3x + 5y + z = -10.....(2)

4x - 3y + 2z = 4......(3)

First, eliminate z by adding (1) and (2)

=> 5x + 4y = -3.........(4)

Then, 2(2) - (3) gives:

2x + 13y = -24..........(5)

Now, eliminate x using 5(5) - 2(4)

=> 57y = -114

i.e. y = -2 => x = 1

substituting into (1) gives:

2 - -2 - z = 7

=> 4 - z = 7

i.e. z = -3

so, the solution (x, y, z) = (1, -2, -3)

:)>

2x - y - z = 7
3x + 5y + z = -10
4x - 3y + 2z = 4
6x + 10y + 2z = -20
5x + 4y = -3
2x + 13y = -24
10x + 8y = -6
10x + 65y = -120
57y = -114
y = -2
x = 1
z = -3