Determine the value of k for which the system of linear equation has infinitely many solutions. Then find all solutions corresponding to this value of K

Question

8x+9y=72

x+ky=9

Determine the value of k for which the system of linear equation has infinitely many solutions. Then find all solutions corresponding to this value of K

Answer 1

Hi!

It will have infinitely many solutions if one of the equations is equal to (the other one times a factor).

8x+9y=72 is eight (factor) times bigger than x+ky=9 (I know that because I know that 72 is eight times bigger than 9).

Just like 72:8=9, you can say that 9:8=k

That’s your answer!! K=9/8 yay!!! 🤩🤩🤩

Answer 2

In order for the system of equations to have infinitely many solutions, x + ky = 9 must be equivalent to 8x+9y=72.

Multiplying the second equation by 8: 8(x + ky = 9)

Distributing the 8: 8x +8ky = 72

Now we need 9 to be equivalent to 8k in order for the system to be equivalent.

In order to see what value of k would make 9 and 8k equivalent, we set them equal to each other.

9 = 8k

Divide both sides by 8: k = 9/8

Therefore , in order for the system of equations to have infinitely many solutions, k must be 9/8