Respuesta :
x = 1; y = 2; z = -1
This involves solving simultaneous equations using elimination method.
- We are given the equations;
x + y - 2z = 5 - - - (eq 1)
-x + 2y + z = 2 - - - (eq 2)
2x + 3y – z = 9 - - - (eq 3)
- Looking at the 3 equations, let's multiply equation 2 by 3 and multiply eq 1 and eq 3 by 1 to get;
x + y - 2z = 5 - - - (eq 4)
-3x + 6y + 3z = 6 - - - (eq 5)
2x + 3y – z = 9 - - - (eq 6)
Add eq 4, 5 & 6 together to get;
10y = 20
y = 20/10
y = 2
- Similarly, let's repeat this proves by multiplying eq 1 by -1 and eq2 & eq 3 by 1 to get;
-x - y + 2z = - 5 - - - (eq 7)
-x + 2y + z = 2 - - - (eq 8)
2x + 3y – z = 9 - - - (eq 9)
Add eq 7, 8 and 9 together to get;
4y + 2z = 6
From earlier, we saw that y = 2. Thus;
4(2) + 2z = 6
8 + 2z = 6
2z = 6 - 8
2z = -2
z = - 2/2
z = - 1
Putting -1 for z and 2 for y into;
x + y - 2z = 5
Gives; x + 2 - 2(-1) = 5
x + 4 = 5
x = 5 - 4
x = 1
Thus; x = 1; y = 2; z = -1
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