To calculate: The solution for the system of provided equations:

kolonelyf4

kolonelyf4

Answered question

2021-11-17

To calculate: The solution for the system of provided equations:
5a2b+3c=10
3a+b2c=7
a+4b4c=3

Answer & Explanation

Melinda Olson

Melinda Olson

Beginner2021-11-18Added 20 answers

(A) 5a2b+3c=10
(B) 3a+b2c=7
(C) a+4b4c 3
Consider (A) or (B):
(A) 5a2b+3c=10
(B) 3a+b2c=7
Multiply (B) with 2:
(A) 5a2b+3c=10
2 (B) - 6a + 2b - 4c = -14
Now, add (A) and (B):
(D) ac=4
Consider (A) and (C):
(A) 5a2b+3c=10
(C) a+4b4c=3
Multiply (A) with 2:
2 (A) 10a - 4b + 6c = 20
(C) a+4b4c=3
Add both the above equastion:
(E) 11a+2c=17
Now consider (D) and (E):
(D) ac=4
(E) 11a+2c=17
Multipy (D) with 2:
2 (D) - 2a - 2c = -8
(E) 11a+2c=17
Now, add both the equastions and solve for a:
9a=9
(dividing both sides by 9)
a=1
Substitute 1 for a in (D):
(1)c=4
Adding 1 to both sides and then dividing by -1,
c=3
c=3
Substitude 3 for c and 1 for a in (A) and solve for b:
5(1)2b+3(3)=10
2b+14=10
Substracting 14 from both sides and then dividing by -2,
2b=4
b=2
2b=4
b=2
So, the values obtained are a=1, b=2 and c=3. Substitute thease values
in each of the provided equations to verify:
First Equation: 5(1)2(2)+3(3) 10
54+9 10
10 10
The result is true.
Second Equation:
-3 (1) + (2) - 2(3) -7
-3 + 2 -6 -7
-7 -7
The result is true.
Third Equation:
(1) + 4 (2) - 4(3) -3
1 + 8 - 12 -3
-3 -3
The result is true.
5a - 2b + 3c = 10
Therefore, the solution of the system of equations 3a+b2c=7 is
a+4b4c=3

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