Consider this system of equations:
2x + y – 3z = 1
x + 2y + 5z = 9
3x – 3y – 10z = 4

The first sub-goal is to derive a system of 2 equations in two variables from the system of 3 equations. Eliminate x by doubling the second equation and subtracting the first equation from this doubled equation.

Question

Consider this system of equations:
 2x + y – 3z = 1
 x + 2y + 5z = 9
 3x – 3y – 10z = 4


The first sub-goal is to derive a system of 2 equations in two variables from the system of 3 equations. Eliminate x by doubling the second equation and subtracting the first equation from this doubled equation.

ranga · Answer

You have 3 equations and 3 unknowns: x, y and z.
Multiply second equation by 2 and subtract equation 1 from it.
You will eliminate the variable x and end up with 1 equation and 2 unknowns y and z.

Then multiply the second equation by 3 and subtract the third equation from it.
You will get another equation in y and z.

You will now have 2 equations and 2 unknowns.

You can try the elimination method again and get rid of one of the variables and then you can solve for the remaining variable.  Then substitute back into the equations and solve for the other two variables.

anonymous · Answer

Okay, that makes a lot more sense.