Answer:
Step-by-step explanation:
x + y = 1........x = 1 - y
2x - y + z = 1
x + 2y + z = 8/3....I am changing this equation...multiplying everything by 3....this gets rid of the fraction.....changes to : 3x + 6y + 3z = 8
now sub 1 - y in for x in both of the other equations
2x - y + z = 1 3x + 6y + 3z = 8
2(1 - y) - y + z = 1 3(1 - y) + 6y + 3z = 8
2 - 2y - y + z = 1 3 - 3y + 6y + 3z = 8
2 - 3y + z = 1 3 + 3y + 3z = 8
-3y + z = 1 - 2 3y + 3z = 8 - 3
-3y + z = -1 3y + 3z = 5
now we have :
-3y + z = -1
3y + 3z = 5
--------------------add
4z = 4
z = 4/4
z = 1 <======
now sub 1 in for z in either of the resulting equations we got
3y + 3z = 5
3y + 3(1) = 5
3y + 3 = 5
3y = 5 - 3
3y = 2
y = 2/3 <===
so we know z = 1 and y = 2/3.....so sub those in to either of the beginning equations to find x
x + y = 1
x + 2/3 = 1
x = 1 - 2/3
x = 3/3 - 2/3
x = 1/3 <===
we need to check this now...
2x - y + z = 1
2(1/3) - 2/3 + 1 = 1
2/3 - 2/3 + 1 = 1
1 = 1 (correct)
so it checks out......x = 1/3 , y = 2/3, and z = 1
