Solving simultaneous linear equation

So here goes!

y + z = 5

x + 3y + z = 10

3x + 2y + z = 10

I'm changing around equation 1 so i get y = 5 - z

Then subbing it into equation 3 and 2 but i'm just not getting the correct answers!

feel free to have a go!

Thanks!

make 2 and 3 =0

x+3y+z-10=0 3x+2y+z-10=0

as these equations are equal (both equal 0) we can write them equal to each other

x+3y+z-10 = 3x+2y+z-10

we can subtract x, z and 2y from both sides and we can add 10 to both sides to give us

y = 2x

Now sub y value into 2

x+3(2x)+z=10

x+6x +z +10

7x+z=10

z=3

sub z value into 1

y+3=5

y=2

sub z and y values into 2

x+3(2)+3 = 10

x+6+3 = 10

x+9 = 10

x=1

x = 1, y = 2 and z = 3

good luck buddy

y + z = 5 (say eq1)
x + 3y + z = 10 (say eq2)
3x + 2y + z = 10 (say eq3)

Multiply eq1 by (-1) and then add up with eq2, we get:
x+2y = 5 (say eq12)

Likewise, Multiply eq1 by (-1) and then add up with eq3, we get:
3x+2y = 5 (say eq13)
from eq12 and eq13, we get: y = 2 and x = 1
From eq1, we get:
z = 3
ans: x = 1; y = 2; z = 3

Verification:
eq1: y+z = 5 = 2+3
eq2: x+3y+z = 10 = 1+6+3
eq3: 3x+2y+z = 10 = 3+4 + 3

y + z = 5 ---------------------------------- 1

x + 3y + z = 10 or
x + 2y+(y + z) = 10; using 1 we get
x+2y = 5 ----------------------------------- 2
Also
3x + 2y + z = 10 or
3x+y+(y+z) = 10; using 1 we get
3x+y = 5 ----------------------------------- 3
Subtracting 3 times 2 from 3, we get
-5y = -10 or y = 2 --------------- 4; using 1 weget
z = 3 --------------------------------- 5
Using 2, we get x = 1 ---------- 6
4,5 and 6 gives us x = 1, y = 2 and z = 3