Question

Solve the following system of simultaneous equation: 7b + 3a = -5 & 4a - 3b - 8 = 0​

Answer 1

The solution to the simultaneous equations 7b + 3a = -5 and 4a - 3b - 8 = 0 involves expressing b in terms of a, substituting it into the first equation, and then solving for a before finding the value of b. The final solution is a = 41 / 37 and b = -4 / 3.

Step-by-step explanation:

To solve the simultaneous equations for the unknowns a and b, let's start with the given system:

1. 7b + 3a = -5
2. 4a - 3b - 8 = 0

Firstly, we can rearrange the second equation to get one of the variables by itself:

1. +3b + 8 = 4a
2. b = (4a - 8) / 3

Now we can substitute the expression for b from equation (4) into equation (1):

1. 7((4a - 8) / 3) + 3a = -5
2. 28a - 56 + 9a = -15
3. 37a - 56 = -15
4. 37a = 41
5. a = 41 / 37

With the value for a found, substitute it back into equation (4) to find b:

1. b = (4(41 / 37) - 8) / 3
2. b = (164 / 37 - 296 / 37) / 3
3. b = -132 / 37 / 3
4. b = -132 / 111
5. b = -4 / 3

The solution of the system is therefore a = 41 / 37 and b = -4 / 3. Eliminate terms where possible to simplify the algebra along the way, and once the solution is found, it's important to check the answer to see if it is reasonable, which we can do by substituting the values of a and b back into the original equations.