Final answer:
To find the value of a + b for the system of equations, we use substitution and end up with a = 0.2 and b = 0.3, leading to a + b = 0.5. However, this does not match the given options.
Step-by-step explanation:
To find the value of a + b for the system of equations given:
- 0.7a − 0.8b = −0.1
- a − 1.4 = −6(b − 0.1), which simplifies to a + 6b = 2
We can solve this system using either substitution or elimination. The second equation can be written as a = 2 - 6b. Now substituting this expression for 'a' in the first equation:
0.7(2 - 6b) − 0.8b = −0.1
1.4 − 4.2b − 0.8b = −0.1
1.4 − 5b = −0.1
5b = 1.4 + 0.1
5b = 1.5
b = 0.3
Once we have the value of 'b', we can substitute back into a = 2 - 6b to find 'a':
a = 2 - 6(0.3)
a = 2 - 1.8
a = 0.2
Finally, we can find the sum of 'a' and 'b':
a + b = 0.2 + 0.3 = 0.5
However, none of the options match our calculated value, which suggests there might be an error in the question, the options provided, or our calculation.