The solution for the simultaneous equations 2x + y - 2z = 12, x + 2y +z =18 and 2x - y + 2z =16 are x = 7, y = 4 and z = 3
Linear equations are equations that have constant average rates of change, slope or gradient
A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2x + y - 2z = 12,
x + 2y +z =18
2x - y + 2z =16
Eliminate y and z in the equations by adding the first and the third equation together
This gives
2x + y - 2z = 12,
+
2x - y + 2z =16
--------------------------
4x = 28
Divide both sides by 4
x = 7
Substitute x = 7 in x + 2y +z =18 and 2x - y + 2z =16
7 + 2y +z =18
2(7) - y + 2z =16
This gives
2y + z = 11
-y + 2z= 2
Multiply -y + 2z= 2 by 2
-2y + 4z= 4
Add -2y + 4z= 4 and 2y + z = 11
5z = 15
Divide by 5
z = 3
Substitute z = 3 in -y + 2z= 2
-y + 2*3= 2
Evaluate
y = 4
Hence, the solution for the simultaneous equations 2x + y - 2z = 12, x + 2y +z =18 and 2x - y + 2z =16 are x = 7, y = 4 and z = 3
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