Question

Determine the values of a an b that make the system dependent

Answer 1

Given the system of equations:

ax + by = -12

7x + 8y = 6

Let's determine the values of a and b that make the system dependent.

Since both equations are dependent, we have:

ax + by = -12

7x + 8y = 6

Apply the formula:`

`(a1)/(a2)=(b1)/(b2)=(c1)/(c2)`

Where:

a1 = a

b1 = b

c1 = -12

a2 = 7

b2 = 8

c2 = 6

Thus, we have:

`(a)/(7)=(b)/(8)=(-12)/(6)`

Thus, for a, consider:

`\begin{gathered} (a)/(7)=(-12)/(6) \\ \\ \text{Cross mutiply:} \\ 6a=-12(7) \\ \\ 6a=-84 \\ \\ \text{Divide both sides by 6:} \\ (6a)/(6)=(-84)/(6) \\ \\ a=-14 \end{gathered}`

For the value of b, we have:

`\begin{gathered} (b)/(8)=(-12)/(6) \\ \\ \text{Cross multiply:} \\ 6b=-12(8) \\ \\ 6b=-96 \\ \\ \text{Divide both sides by 6:} \\ (6b)/(6)=(-96)/(6) \\ \\ b=-16 \end{gathered}`

Therefore, the values of a and b that make the system dependent are:

a = -14

b = -16

ANSWER:

a = -14, b = -16