Solve the following system of equations. (please help iam stuck)?

Question

x + 2y − 6 = z
3y − 2z = 7
4 + 3x = 2y − 5z

Answer 1

x+2y-z=6 ---------(1)
3y-2z=7 ----------(2)
3x-2y+5z=-4 -------(3)
from (1), x=z+6-2y -------(4)
from (3), x=(2y-5z-4)/3 -------(5)
solving (4) & (5), we have: 4y-4z=11 -----(6)
solving (2) & (6), we have : y=3/2 and z=-5/4
by substituting these values in (1) or (3), we have x=7/4
hence the values which satisfy all the three equations simultaneously are: x=7/4, y=3/2, z=-5/4

Answer 2

You have three equations in three unknowns, so this is just a matter of substitution. First, solve one of the equations for one unknown. The first one is already solved for you. It gives you an expression for z.

Now, substitute that into the other two equations. Solve one of those for another variable. For example, solve the second equation for y. Now, substitute that answer into the third equation. You now have an equation only in x. Solve that to get the value for x.

Using that, plug that back into your intermediate equation and get the value for y. From that, you get the value for z.

Don't forget to show your work.

Answer 3

first set each equation to solve for each variables: x,y,z.
z equation (eqn) is given.
2nd, rearrange using substitution of the given z eqn to get y eqn :
3y-2(x+2y-6)=7 --> 3y-2x-4y+12=7 --> [ y=5-2x ]
3rd use these two eqns: y & z, to substitute the y & z variables of your 3rd eqn to get your x value, you get as follows:

4+3x=2(5-2x)-5(x+2y-6)
=10-4x-5x-10y+30 *** substitute the y again w/ *y eqn*
=10-4x-5x-10(5-2x)+30
4+3x= 11x-10
[ x=1.75 ] *** :) x is solve and you can plug/chug using x
value to get the values for y & z