Question

What is the solution to the system of equations?
-2x-3y+z=-6
z=6
3x-y+z=13
A.(3, 2, 6)
B.(3, 2, –6)
C.(3, –2, 6)
D.(–3, 2, 6)

Answer 1

Well if we already know that z = 6 we can plug that into both the equations we have

-2x - 3y + z = -6

becomes

-2x - 3y + 6 = -6

subtract 6 from both sides

\(\large \color \red{-2x - 3y = -12}\)


And the second equation we have is

3x - y + z = 13

This will become

3x - y + 6 = 13

subtract 6 from both sides again

\[\large \color \red{3x - y = 7}\]

Now we just have a system of 2 equations...can you solve them?

Answer 2

you type fast johnweldon

Answer 3

no, i am horrible at these. i always get the wrong answer.

Answer 4

My computer was lagging so it wasn't registering @texaschic101 lol

And okay we'll work through it @alo03209

Answer 5

she skipped out on you

Answer 6

The nerve! haha

Answer 7

lol

Answer 8

okay.

Answer 9

-2x - 3y = -12
3x - y = 7 --->(-3)
------------------
-2x - 3y = -12
-9x + 3y = -21 (result of multiplying by -3)
------------------add
-11x = - 33
x = 3
now sub 3 in for x
3x - y = 7
3(3) - y = 7
9 - y = 7
-y = -2
y = 2

check...
3x - y = 7
3(3) - 2 = 7
9 - 2 = 7
7 = 7 (correct)

x = 3, y = 2, z = 6

any questions ?

Answer 10

pretty self explanitory , thanks.

Answer 11

glad to help :)