Question

solve the system of equations
x+y+z=13
-2x-y+z=-4
x-2y-z=-18

Answer 1

x+y+z=13
-2x-y+z=-4
Add.
-3x + 2z = 9
Then.
(-2x-y+z=-4)(times) -2
4x+2y-2z=8
x-2y-z=-18
Add.
5x - 3z = -10
Now
(-3x + 2z = 9)(times)3
-9x +6z = 27
(5x - 3z = -10)(times)2
10x - 6z = -20
~~~~~~~~~~~~~~~

-9x +6z = 27
10x - 6z = -20
Add.
x = 7
~~~~~~~~~~~~~~~~~
Now substitute x in 5x - 3z = -10
5(7) - 3z = -10
35 - 3z = -10
Subtract 35 on both sides
-3z = -45
Divide by -3 on both sides
z = 15
~~~~~~~~~~~~~~~~~~~~~~
Now substitute x and z in the first equation.
7 + y + 15 = 13
Combine like terms
22 + y = 13
Subtract 22 on both sides
y = -9
~~~~~~~~~~~~~~~~~
Substitute all variables in every equation to see if they are correct.
x = 7
y = -9
z = 15

7+(-9)+15=13
7-9=-2+15=13
13=13 Correct!
-2(7)-(-9)+15=-4
-14+9=-5+15=10
10=-4 Incorrect!!
7-2(-9)-15=-18
7+18=25-15=10
10=-18 Incorrect!!
Not sure where I went wrong....
@Best_Mathematician Can you help me find where I went wrong?

Answer 2

@jim_thompson5910 Help me find my mistake?

Answer 3

when you add equations 1 and 2 you should get

x+y+z=13
-2x-y+z=-4
------------
-1x+0y+2z=9

which turns into

-x+2z = 9

Answer 4

Ohhhh! Duh!

Answer 5

looks like he/she found what she want! still need help...just tag me in comment

Answer 6

x+y+z=13
-2x-y+z=-4
Add.
-x + 2z = 9
Then.
(-2x-y+z=-4)(times) -2
4x+2y-2z=8
x-2y-z=-18
Add.
5x - 3z = -10
Now
(-x + 2z = 9)(times)3
-3x +6z = 27
(5x - 3z = -10)(times)2
10x - 6z = -20
~~~~~~~~~~~~~~~

-3x +6z = 27
10x - 6z = -20
Add.
7x = 7
x=1
~~~~~~~~~~~~~~~~~
Now substitute x in 5x - 3z = -10
5(1) - 3z = -10
5 - 3z = -10
Subtract 5 on both sides
-3z = -15
Divide by -3 on both sides
z = 5
~~~~~~~~~~~~~~~~~~~~~~
Now substitute x and z in the first equation.
1 + y + 5 = 13
Combine like terms
6 + y = 13
Subtract 6 on both sides
y = 7
~~~~~~~~~~~~~~~~~
Substitute all variables in every equation to see if they are correct.
x = 1
y = 7
z = 5

1+7+5=13
8+13=13
13=13 Correct!
-2(1)-7+5=-4
-2-7=-9+5=-4
-4=-4 Correct!
1-2(7)-5=-18
1-14=-13-5=-18
-18=-18 Correct!