ALGEBRA QUESTION?

b-c=-30
c=b+30

a-b=10
a=10+b

a+c=20

10+b +b +30=20
2b+40=20
2b=-20
b=-10

c=b+30
c=-10+30
c=20

a=10+b
a=10-10
a=0

a - b = 10 …… [1]
a + c = 20 …… [2]
b - c = -30 …… [3]

[1] + [2] + [3] :
a - b + a + c + b - c = 0
2a = 0
a = 0

The answer: d. 0

If a - b = 10,,a + c = 20,and b - c = -30 then find a
a - c = -20,
a = 0
Answer choice:
d. 0

(1) : a - b = 10

(2) : a + c = 20

(3) : b - c = - 30


You calculate (1) - (2)

(a - b) - (a + c) = 10 - 20

a - b - a - c = - 10

b + c = 10 → recall (3): b - c = - 30 → b = c - 30

c - 30 + c = 10

2c = 40

→ c = 20


Recall (3): b - c = - 30

b = c - 30 → recall: c = 20

b = 20 - 30

→ b = - 10


Recall (1) : a - b = 10

a = b + 10 → recall: b = - 10

a = - 10 + 10

→ a = 0

If a - b = 10, a + c = 20, and b - c = -30 then find a.
b + c = 10, b = -10
Answer choice:
d. 0

Add the first and third equations and you get a - c = -20. Add this with the second equation and you get 2a = 0, which makes a = 0. D).

a - b = 10,................(1)

a + c = 20, ................(2)

b - c = -30..................(3)

Add (1) and (3)

a - c = -20 ................(4)

Add (2) and (4)

2a = 0

a = 0 ..............[ b = -10, c = 20 ]

a–b=10
a+c=20
b–c=–30

–a+b = –10
a+c = 20
add
b+c = 10
b–c = –30
add these two
2b = –20
b = –10
substitute
a–b = 10
a–( –10) = 10
a+10 = 10
a = 0 ⬅
a–b = 10
–b = 10
b = –10 ⬅
b+c = 10
–10 + c = 10
c = 20 ⬅

check
a–b=10
0+10 = 10 ok
a+c=20
0+20=20 ok
b–c=–30
–10–20 = –30 ok

1

a - b = 10
a + ( b + 30 ) = 20

a - b = 10
a + b = - 10________add

2a = 0
a = 0
b = - 10
c = 20

a-b=10 ----(1)
a+c =20 ----(2)

subtract (2) from (1)
-b-c = -10
multiply both sides by -1

b+c = 10
b-c = -30
add:
2b = -20
b=-10

a-b=10 -----(1)
a-(-10) = 10
a+10=10
a=0