Question

Given that 3a-2b=8 and 4a+4b=24, what is the value of a-b ?

Answer 1

To solve for a and b from the system of equations 3a-2b=8 and 4a+4b=24, we use elimination and substitution to find that a=4 and b=2, which gives us the value of a-b as 2.

Step-by-step explanation:

We need to find out the value of a-b from the given equations 3a-2b=8 and 4a+4b=24. To solve the system of equations, we can use the method of elimination or substitution. For simplicity, let's try to eliminate one of the variables.

First, let's manipulate the second equation to make it easier to eliminate a variable:

1. Multiply the first equation by 2 to get 6a-4b=16.
2. Multiply the second equation by 1 to keep it the same: 4a+4b=24.
3. Now add both equations: (6a - 4b) + (4a + 4b) = 16 + 24, which simplifies to 10a=40.
4. Solving for a gives us a=4.

Now we can plug the value of a into either of the original equations to find b. Let's use the first equation:

1. Substitute a=4 into 3a-2b=8: 3(4) - 2b = 8.
2. This simplifies to 12 - 2b = 8.
3. Subtract 12 from both sides: -2b = -4.
4. Divide by -2 to find b=2.

Finally, we can calculate a-b:

1. Substitute a=4 and b=2: 4 - 2.
2. The answer is a-b=2.

The value of a-b is 2.