107k views
2 votes
Determine the values of a an b that make the system dependent

Determine the values of a an b that make the system dependent-example-1

1 Answer

1 vote

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

User BSMP
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories