a+3b=12 2b-a=3 what is b^2-a^2?

2009-04-17 3:37 pm
a+3b=12
2b-a=3
what is b^2-a^2

回答 (13)

2009-04-17 3:43 pm
✔ 最佳答案
a+3b=12......(1)
2b-a=3......(2)
(1)+(2): 5b = 15 => b = 3, a = 2b-3 = 3
So, b^2-a^2 = 3^2 - 3^2 = 0
2009-04-17 3:47 pm
Value of a:
(12 - a)/3 = (a + 3)/2
24 - 2a = 3a + 9
5a = 15
a = 3

Value of b:
= (12 - 3)/3
= 9/3 or 3

Value of b² - a²:
= 3² - (3)²
= 9 - 9
= 0

Answer: b² - a² = 0

Proof (2nd equation):
2(3) - 3 = 3
6 - 3 = 3
3 = 3
2009-04-18 11:07 am
a + 3b = 12
2b - a = 3

a + 3b = 12
a = 12 - 3b

2b - a = 3
2b - (12 - 3b) = 3
2b - 12 + 3b = 3
2b + 3b = 12 + 3
5b = 15
b = 15/5
b = 3

a + 3b = 12
a + 3(3) = 12
a = 12 - 9
a = 3

b^2 - a^2 (a = 3 , b = 3)
= 3^2 - 3^2
= 0
2009-04-17 3:55 pm
a+3b=12
2b-a=3

a+3b=12
-a+2b=3
-----------------
...5b=15
b=3

plug in to equation 1

a+3(3)=12
a+9=12
a=12-9
a=3

so

b^2-a^2=3^2-3^2=9-9=0 answer//
2009-04-17 3:53 pm
a= 3
b= 3

b^2 - a^2 = 9 - 9 = 0
2009-04-17 3:46 pm
First, find a and b
I'll switch the equations around a bit...

a+3b=12
-a+2b=3 add the equations

5b=15
b=3

substitute in b to equation 1

a+3(3)=12
a+9=12
a=3

a²-b²=3²-3²=9-9=0
2009-04-17 3:46 pm
a + 3b = 12 (Equation 1)

2b - a = 3 (Equation 2)

Rearrange equation 1 to give:

a = 12 - 3b

Substitute for "a" in equation 2

2b - (12 - 3b) = 3

Expand

2b - 12 + 3b = 3

Simplify

5b = 15

Therefore, b = 3

Now, plug the value for "b" into equation 1

a + 3x3 = 12

Rearrange and simplify

a = 3

So, finally...

a^2 - b^2 = 3^2 - 3^2 = 9 - 9 = 0
2009-04-17 3:45 pm
a+3b=12 and 2b-a=3
a+3b+2b-a= 12+3
5b = 15
b = 15/5
b = 3
a+3b=12
a = 12-3b
a = 12-3(3)
a = 12-9
a = 3
b^2-a^2 = 3^2 - 3^2 = 9 - 9 =0
2009-04-17 3:43 pm
0
2009-04-17 3:43 pm
Add the two equations:

5b = 15.

So b=3.

Rearrange the first equation:

a = 12 -3b

and because b=3, we get a=12-9=3.

So b^2-a^2 = 3^2 -(3)^2 = 9-9 = 0.
參考: Mathematics professor


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