By using the substitution method, we conclude that the solution to the system is x = 7, y = -2, z = 2.
How to solve the system of equations?
Here we have the system:
x + 2y = 3
-2x - 3y + 2z = 2y
-2x + z = 4
To solve this, first, we need to isolate one of the variables in one of the equations. We can isolate x on the first one:
x = 3 - 2y
Now we can replace that in the other two equations:
-2*( 3 - 2y) - 3y + 2z = 2y
-2*( 3 - 2y) + z = 4
Now we simplify these two:
-6 - y + 2z = 0
-6 - 4y + z = 4
Now we can isolate z on the second equation:
z = 4 + 4y + 6 = 4y + 10
And replace it on the other equation:
-6 - y + 2*(10+ 4y ) = 0
-6 - y + 20 + 8y = 0
7y + 14 = 0
y = -14/7 = -2
Now that we know the value of y, we can find the values of x and z.
z = 4y + 10 = 4*(-2) + 10 = 2
x = x = 3 - 2y = 3 - 2*(-2) = 7
So the solution is:
x = 7, y = -2, z = 2.
If you want to learn more about systems of equations:
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