3a+5b=1,4a+2b=6?

Question

solve by elimination

Answer 1

3a + 5b =1- - - - - -Equation 1
4a + 2b = 6- - - - - Equation 2
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Multiply equatio 1 by - 1 and equation 2 by 5

3a + 5b = 1
- 2 (3a) + - 2(5b) = - 2(1)

- 6a + (-10b)= - 2

- 6a - 10b = - 2. . .New equation 1

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4a + 2b = 6

5(4a) + 5(2b) = 5(6)

20x + 10b = 30. . . New equation 2

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New equation 1 and new equation 2

Elimination of b, Solving for a

-6a - 10b = - 2
20a + 10b = 30
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14a = 28

14a/14 = 28/14

a = 2

The answer is a = 2

Insert the a value into equation 1

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Solving for b

3a + 5b = 1

3(2) + 5b = 1

6 + 5b = 1

6 + 5b - 6 = 1 - 6

5b = -5

5b/5= - 5/5

b = - 1

The answer is b = - 1

Inserty the b value into equation 1

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Check for equation 1

3a + 5b = 1

3(2) + 5(- 1) = 1

6 + (-5) = 1

6 - 5 = 1

1 = 1

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Check for equation 2

4a + 2b = 6

4(2) + 2(- 1) = 6

8 + (- 2) = 6

8 - 2 = 6

6 = 6

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The solution set { a, b ]

The solution set is { 2, - 1 }

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Answer 2

ab + 3a + 2b +6 the 1st term is ab as a bring about the bracketed factorization the 1st ingredient is a * b (a + ?) (b + ?) The final term in the unique function is 6 which could be factored as a million * 6 or 2 * 3 As there's a 3a and a 2b in the unique function then the climate of 6 are 2 * 3 and as there must be 3a the three ought to be in the (b + ?) area of the factorization So the climate are (a +2)(b +3)

Answer 3

3a + 5b = 1
4a + 2b = 6

4(3a) + 4(5b) = 4(1)
3(4a) + 3(2b) = 3(6)

12a + 20b = 4
12a + 6b = 18

12a + 20b = 4
-1(12a) + -1(6b) = -1(18)

12a + 20b = 4
-12a - 6b = -18

12a - 12a + 20b - 6b = 4 -18
14b = -14
b = -1

By substituting -1 for b we get: 3a + 5(-1) = 1
3a + -5 = 1
3a = 1 + 5
3a = 6
a = 3

Thus a = 3 and b = -1

I hope the explanation helps.

Answer 4

3a+5b=1 multiply by -4
-12a-20b=-4
4a+2b=6 multiply by 3
12a+6b=18
-12a-20b=-4 add
-14b=14 divide by -14
b=-1
substitute
3a+-5=1 add 5
3a=6 divide by 3
a=2
solution is (2,-1)
check
4*2+2*-1=6
8-2=6

Answer 5

3a+5b=1
3a=1-5b
a=(1-5b)/3

substitute for "a" in the other equation and solve for "b"
4((1-5b)/3)+2b=6

b=2
a=-1

Answer 6

-4(3a+5b=1)
3(4a+2b=6)
=========
-12a-20b=-4
12a+6b=18
=========
-14b=14
b=-1
3a+5(-1)=1
3a-5=1
3a=6
a=2
(2,-1)

Check:
3(2)+5(-1)=1
6-5=1
1=1

4(2)+2(-1)=6
8-2=6
6=6

Answer 7

12a+20b=4
-12a-6b=-18
adding
14b=-14
b=-1
sub
3a-5=1
3a=6
a=6/3=2
a=2,b=-1