x-y=2xy,y+z=3yz,z-x=4xz
Answers
Step-by-step explanation:
x + y + z = 4
x - 2y - z = 1
2x - y - 2z = -1
First, let's eliminate x. This can be done by taking the equations two at a time and using the elimination method to cancel out x each time.
Start with the first and second equations. Multiply the first equation by -1 and add it to the second equation to eliminate x.
-x - y - z = -4
x - 2y - z = 1
-3y - 2z = -3
Now let's use the first and third equations. Multiply the first equation by -2 and add it to the third equation.
-2x - 2y - 2z = -8
2x - y - 2z = -1
-3y - 4z = -9
Next, use the two equations created by those steps to eliminate y. Multiply the first equation by -1 and add it to the second.
3y + 2z = 3
-3y - 4z = -9
-2z = -6
Solve the resulting equation for z.
-2z = -6
z = 3
Substitute 3 for z in one of the two y-z equations and solve for y.
-3y - 2z = -3
-3y - 2(3) = -3
-3y - 6 = -3
-3y = 3
y = -1
Finally, substitute -1 for y and 3 for z in one of the original equations and solve for x.
x + y + z = 4
x + (-1) + 3 = 4
x + 2 = 4
x = 2
The answer is (2, -1, 3).
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