Question

Which ordered triple is a solution of the following linear system?: 2x+3y+2z=26 −x+7y−z=21 3x+2y−5z=13

Answer 1

For this case we have the following system of equations:

`2x + 3y + 2z = 26 -x + 7y-z = 21 3x + 2y-5z = 13`
From equation 2 we can clear z:

`z = -x + 7y-21`
We substitute the values of z in equations 1 and 3:

`2x + 3y + 2 (-x + 7y-21) = 26 3x + 2y-5 (-x + 7y-21) = 13`
From here, we obtain a system of two equations with two unknowns, whose graphical solution is given by the intersection of both lines:

`x = 5 y = 4`
Note: See attached image for the graphic solution
We now look for the value of z replacing the found values of the graphic solution:

`z = -x + 7y-21 z = -5 + 7 * (4) -21 z = 2`
Therefore, the triple ordered solution is:

`(x, y, z) = (5,4,2)`
Answer:

`(x, y, z) = (5,4,2)`
See attached image