Question

Solve the system by substitution.

-x-y-z=-8
-4x+4y+5z=7
2x+2z=4

Answer 1

Lets take 2x + 2z = 4
Dividing each term by 2 we get
x + z = 2 => x = 2 - z

Answer 2

Now lets substitute x in any one of the first two equations.

Lets take -x -y -z = -8

Multiply each term with minus sign we get x + y + z = 8

now get x = 2-z in place of x in the above equation

Answer 3

2 - z + y + z = 8 => 2 + y = 8 => y = 6

Answer 4

Now substitute x and y in second equation that is -4x + 4y + 5z = 7

-4(2 - z) + 24 + 5z = 7

-8 + 4z + 24 + 5z = 7
9z = 7 - 16
9z = -9
z = -1

Answer 5

Now Substitute z = -1 in x = 2 - z we get x = 2 - (-1) = 2 + 1 = 3

Answer 6

Thank you so much I was stuck on this question for the longest. Can you help me with another one?

Answer 7

Sure np

Answer 8

Solve the system of elimination

-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

Answer 9

Lets take first and 3rd equations and add them

Answer 10

Ok did you multiply the second equation?

Answer 11

No I didnt I just added first and 3rd equations

Answer 12

Now lets subtract first two equations

Answer 13

-2x + 2y + 3z = 0
-2x -y + z = -3
(+) (+) (-) (+)
Subtracting these 2

3y +2z = 3

Answer 14

Now take equation 4 and 5 which we got as resultant in above two equations

Answer 15

5y + 6z = 5
3y + 2z = 3

Now Multiply equation 3y + 2z = 3 with 2 and subtract from 5y + 6z = 5

5y + 6z = 5
9y + 6z = 9
(-) (-) (-)
............................
-4y = -4 => y = 1

Substitute y = 1 in 3y + 2z = 3
3 + 2z = 3
2z = 0 => z = 0

Answer 16

Now Substitute y and z values in any of the given 3 equations to get x value

Answer 17

-2x + 2y + 3z = 0
-2x + 2 =0
-2x = -2
x = 1

Answer 18

1 ,1 , 0 are the solutions for x, y , z

Answer 19

thank you sooo much

Answer 20

Anytime !