Question

Solve the system of equations using substitution. Write your answer as an ordered triple in the form (x, y, z).

X+ y + z = 2
4x + 5y + z = 12
2x = -4

Answer 1

X+y+z=2 equation 1

4x + 5y + z = 12 equation 2

2x = -4 equation 3

Explanation:

step 1 :

from equation 3 : 2x = -4

x= -4/2 = -2

step 2:

sub value x = -2 in equation 1

y + z = 4 _______ equation 4

step 3:

sub value of x in equation 3

5y + z = 20 _________ equation 4

solve equation 3 and 4

y + z = 4

5y + z = 20 sign change

__(-)_________

-4y = -16

__________

y = 4

substitute x = -2 & y = 4 in equation 1

z = 0

Hence x = -2 , y = 4 & z = 0

Answer 2

(x, y, z) = (-2, 4, 0)

Explanation:

Solving the last equation first, we have ...

2x = -4

x = -2 . . . . . divide by 2

__

Putting this in the first equation, we can write an expression for z:

-2 +y +z = 2

z = 4 -y . . . . . . . add 2-y

__

Putting this in the second equation, we have ...

4(-2) +5y +(4 -y) = 12

-4 +4y = 12

-1 + y = 3 . . . . . divide by 4

y = 4 . . . . . . . . add 1

__

Substituting this into the equation for z, we have ...

z = 4 - 4 = 0

The solution is (x, y, z) = (-2, 4, 0).