Step-by-step explanation:
let's solve it by eliminating method
first we will eliminate x by using first and second equation
multiply second equation by -2
-2 × (x+3y+z) = 8 ➡ -2x -6y-2z = -16
now add it up to first equation
2x-2y+4z -2x-6y-2z = 2 -16 ➡ 2z -8y = -14
now using thus new equation with 3rd one to get rid of z
multiply 3rd equation by 2
2 × (3y-z) = 5 ➡ 6y -2z = 10
add this to the new equation we found
6y -2z + 2z -8y = 10 -14 ➡
now use y to find the value of z in the 3rd equation
3×2 -z = 5
lastly
x + 3×2 + 1 = 8
Answer:
x = 1, y = 2, z = 1.
Step-by-step explanation:
From the third equation:
3y = z + 5
Substitute for 3y in the second equation:
x + z + 5 + z = 8
x + 2z = 3...............(1)
Multiply the first equation by 3 and the second by 2 and add, we get:
6x - 6y + 12 z = 6
2x + 6y + 2z = 16 Adding:
8x + 14z = 22
4x + 7z = 11 ..............(2)
Now multiply equation (1) by -4:
-4x - 8z = -12 ...........(3) Adding (2) and (3):
-z = -1
z = 1.
Substituting for z in (2):
4x + 7(1) = 11
4x = 4
x = 1.
Now substitute x = 1 and z = 1 in the original first equation to find y:
2(1) - 2y + 4(1) = 2
-2y = 2 - 2 - 4 = -4
y = 2.
