Question

If (a,b) is a solution to the system 0.7a−0.8b=−0.1 and a−1.4=−6(b−0.1), what is the value of a+b?

a. 1.2
b. 1.5
c. 1.8
d. 2.1

Answer 1

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.