3a+b=8 3a2+b2=28?

Answer 1

a=1, b=5 or a=3,b=-1

Answer 2

Are those supposed to exponents in the second equation?
3a + b = 8
3a^2 + b^2 = 28
Solve for b in the first equation by subtracting 3a from each side
b = -3a + 8
Plug that in for b in the second equation
3a^2 + (-3a+8)^2 = 28
Use FOIL to simplify on the left side
3a^2 + 9a^2 - 48a + 64 = 28
Subtract 28 from each side and combine like terms
12a^2 - 48a + 36 = 0
Divide everything by 12
a^2 - 4a + 3 = 0
Factor
(a-1)(a-3) = 0
a = 1 or a = 3
Plug those in for a in the equation
b = -3a + 8
For a = 1
b = -3(1) + 8 so b = 5
For a = 3
b = -3(3) + 8 so b = -1
Answer: (1,5) or (3,-1) where the first number is a and the second number is b.

Answer 3

3a+b=8
3a^(2)+b^(2)=28

take the first equation and solve for b:
3a+b=8
b = 8 - 3a

now plug that value for b into the second equation:
3a^(2)+b^(2)=28
3a^(2) + (8-3a)^(2) = 28

now multiply out (8-3a)^(2)
3a^(2) + (8-3a)(8-3a) = 28
3a^(2) + 64 - 48a + 9a^(2) = 28

now combine like terms:
3a^(2) + 9a^(2) - 48a + 64 = 28
12a^(2) - 48a + 64 = 28

now subtract 28 from both sides:
12a^(2) - 48a + 64 - 28 = 0
12a^(2) - 48a + 36 = 0

now factor the quadratic:
12(a^(2) - 4a + 3) = 0
12(a - 3)(a - 1) = 0

set each part = to 0 and solve for a:
a-3 = 0, a-1 = 0
a = 3 and a = 1

now take one value for a and plug it into the first equation:
b = 8 - 3a
b = 8 - 3(3)
b = 8 - 9
b = -1

so when a = 3, b = -1

take the other value of a and plug it into the same equation:
b = 8 - 3a
b = 8 - 3(1)
b = 8 - 3
b = 5

so when a = 1, b = 5

these are you answers:
a = 3, b = -1
a = 1, b = 5

Answer 4

3a + b = 8 ... (1)
3a2 + b2 = 28 ... (2)

Squaring Eqn 1, we get,

9a2 + 6ab + b2 = 64 ... (3)

Now equating eqn 2 & 3, we get,

Subtracting (2) from (3) we get,

6a2 + 6ab = 36

a2 + ab = 6

a(a + b) = 6

therefore,
a = 6 or a + b = 6

if a = 6; then b = 0

now, since a + b = 6, it can be rewritten as b = 6 - a

substituting b = 6 - a in eqn (1), we get
a = 1; b = 5

Hence the solution is

If a = 6, b = 0
& if a = 1, b = 5

Answer 5

situation #a million move the like words to the smae portion of the equals mark. this elements a million/2a - a million/4a = -4 +2. This equals a million/4a = -2. Then move the large type with the a to the dissimilar section. (this elements -2 divided by skill of utilizing a million/4.) it really is likewise reminiscent of a= -2 x 4/a million it truly is reminiscent of a = -8. situation #2 upon getting a binomial, 3a + 4, it truly is squared, you take advantage of the formulation FOIL. You multiply the first words, then the OUTER words, then the interior words, then the finest words. (3a +4) (3a+4) will change into (3a x 3a) + (3a x 4) + (4 x 3a) + (4 x 4). this elements 9a<2 + 12 a + 12a+ 16. Then assemble like words and also you get the 24a contained in the middle time period.

Answer 6

At least if the variable "a" and "b" got these two values:
a=1 --> b=5

3 (1)*(1) + (5)*(5)
= 3 + 25
= 28

a=3 --> b=-1
3 * (3) * (3) + (-1) * (-1)
= 27 + 1
= 28

// *****************************************************
THIS IS FOR:
// *****************************************************
3*a*a + ( 64 - 48*a + 9*a*a ) = 28
==>
3*a*a - 48*a + 36 = 0
==>
a*a - 4*a + 3 = 0

where
a = 3
and
a = 1.

But like, b = 8 - 3a
b(a=3) = 8 - 3 = 5
b(a=1) = 8 - 9 = -1

// *****************************************************
ALSO THINK OF THE FOLLOWING:
// *****************************************************

As if "a" is equal to the parameter, "t"
so "b" is,
b = 8 - 3t

Then, to satisfy the other constraint, "b" should be:
b = sqrt ( 28 - 3 * t * t )
where t <= sqrt ( 28 / 3) = 3.05505046330389
where "t" is less than or equal to 3.05505046330389.

Example #1:
t=2
a=2
b= sqrt(28 - 3*2*2) = sqrt(28-12) = sqrt(16) = 4

Then
3*a*a + b*b
= 3*2*2 + 4*4
= 12 + 16
= 28

Example #2:
t=0.5
a=0.5
b= sqrt(28 - 3*0.5*0.5) = 5.22015325445528

Then
3*a*a + b*b
= 0.75 + 27.25
= 28

Answer 7

3a + b = 8
3a^2 + b^2 = 28

3a + b = 8
b = -3a + 8

3a^2 + (8 - 3a)^2 = 28
3a^2 + ((8 - 3a)(8 - 3a)) = 28
3a^2 + (64 - 24a - 24a + 9a^2) = 28
3a^2 + (64 - 48a + 9a^2) = 28
3a^2 + 64 - 48a + 9a^2 = 28
12a^2 - 48a + 64 = 28
12a^2 - 48a + 36 = 0
12(a^2 - 4a + 3) = 0
a^2 - 4a + 3 = 0
(a - 3)(a - 1) = 0
a = 3 or 1

b = -3(3) + 8 = -9 + 8 = -1
b = -3(1) + 8 = -3 + 8 = 5

ANS :
a = 3
b = -1
or
a = 1
b = 5

Answer 8

3a+b=8 => b=8-3a

3a^2+b^2=28
3a^2+(8-3a)^2=28
3a^2+64-48a+9a^2=28
12a^2 - 48a + 36 = 0
a^2 - 4a + 3 = 0
(a-3)(a-1) = 0
a = 3 or 1

When a=3, b=8-3(3) = -1
When a=1, b=8-3(1) = 5

Answer 9

3a+b=8.............(1)
3a^2+b^2=28....(2)
from (1) b=8-3a
substituting in (2)
3a^2+(8-3a)^2=28
3a^2+64-48a+9a^2=28
12a^2-48a+36=0
dividing by 12
a^2-4a+3=0
(a-3)(a-1)=0
a=3 or 1
when a=3 b=-1 and when a=1 b=5

Answer 10

3a+b=8.............(1)
3a^2+b^2=28....(2)
from (1) b=8-3a
substituting in (2)
3a^2+(8-3a)^2=28
3a^2+64-48a+9a^2=28
12a^2-48a+36=0
dividing by 12
a^2-4a+3=0
(a-3)(a-1)=0
a=3 or 1
when a=3 b=-1 and when a=1 b=5