Question

What is the solution of the following system of equation 2a + 3b =12 a=1/2 b -6

Answer 1

The solution of the system of equations 2a + 3b = 12 and a = 1/2 b - 6 is determined by substitution, resulting in a = -5 and b = 4.

Step-by-step explanation:

The solution to the system of equations 2a + 3b = 12 and a = 1/2 b - 6 requires substitution and algebraic manipulation. By substituting the value of 'a' from the second equation into the first, we can solve for 'b'. Once 'b' is found, we can substitute it back into the second equation to find the value of 'a'.

1. Begin by substituting a = 1/2 b - 6 into the first equation: 2(1/2 b - 6) + 3b = 12.
2. Simplify and solve for 'b': b = 4.
3. Substitute 'b' back into the second equation to find 'a': a = -5.

The solution to the system of equations is a = -5, b = 4.