Solve for x, y and z, given the following equations: x + y + z = 6 2x - y + 3z = 9 -x + 2y + 2z = 9
3 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
We have to solve for x, y and z using
x + y + z = 6 … (1)
2x –y + 3z = 9 … (2)
-x + 2y + 2z = 9 … (3)
Add (1) and (3)
=> 3y + 3z = 15
=> y + z = 5
Substitute this in (1)
=> x + 5 = 6
=> x = 1
substitute this in (2)
=> 2 – y + 3z = 9
=> 2 – (5 – z) + 3z = 9
=> 2 – 5 + z + 3z = 9
=> -3 + 4z = 9
=> 4z = 12
=> z = 3
y + z = 5
=> y = 5 – 3
=> y = 2
Therefore x = 1, y = 2 and z = 3.
neela | High School Teacher | (Level 3) Valedictorian
To Solve for x,y,z
x+y+z=6...............(1)
2x-y+3z=9............(2)
-x+2y+2z=9...........(3)
(2)+(1): 3x+4z = 15.....(4)
2(2)+(3): 4x-x 6z+2z = 18+9 = 27.
3x+8z = 27.....(5).
(5)-(4): 4z = 27-15 = 12.
z = 12/4 = 3. Put z= 3 in (4): 3x+4*3 = 15.
=> 3x= 15-12 -= 3. So x= 3/3 = 1.
Put x= 1 and z = 3 in (1): 1+y+3 =6. So y = 6-4 = 2.
So x= 1.y=2 and z = 3.
giorgiana1976 | College Teacher | (Level 3) Valedictorian
x+y+z=6 (1)
2x-y+3z=9 (2)
-x+2y+2z=9 (3)
We'll start by adding 1 and 3 together to eliminate x.
x + y + z - x + 2y + 2z = 6 + 9
We'll combine like terms:
3y + 3z = 15 (4)
We'll multiply the equation (1) by –2 and we'll add (1) and (2) together to eliminate the x.
-2x - 2y - 2z + 2x - y + 3z = -12 + 9
We'll combine like terms:
-3y + z = -3 (5)
We'll add (4) and (5):
3y + 3z -3y + z = 15 - 3
4z = 12
z = 3
y + z = 5
y = 5 - z
y = 5 - 3
y = 2
x + 5 = 6
x = 6 - 5
x = 1
The solution of the system is {1 ; 2 ; 3}.