Question

For what value of K will the system of equations given below have no solution?


2x + 5y = 9
-3x - K y = 4

Answer 1

please help

Answer 2

What class is this for? Linear algebra?

Answer 3

i don't know dear. It is in compass test.

Answer 4

so you can help me?

Answer 5

Ok. I was just wondering what methods we have available.
To make this have no solutions, what we need is the same thing on the left side of the equations but something else on the right. So what if we multiply the first equation by -3 and the second by 2 (to make the x coefficients the same)
-6x-15y = -27
-6x-2Ky = 8
Now, what if K = 7.5? Then we have
-6x-15y = -27
-6x-15y = 8
so -27 = 8, which is no good.

Answer 6

its result is 35/2 but i don't know how to solve

Answer 7

We're looking for a value for K that results in "no solutions." If we plug in 7.5 for K, we end up with the equation -27 = 8, which is never true no matter what values of x and y we use. So if K = 7.5, we have no solutions, so that's the answer.

Answer 8

but its answer is 35/2

Answer 9

Maybe I made a mistake somewhere, let me double-check :)

Answer 10

ok honey

Answer 11

Here's another method, but it's getting me the same answer:
Take the first equation and solve for y:
2x+5y=9
5y=9-2x
y=9/5 - 2x/5
Then plug into the second equation:
-3x-K(9/5-2x/5) = 4
-3x-(9/5)K +(2/5)Kx = 4
(-3+(2/5)K)x = 4+(9/5)K
\[x = \frac{4+(9/5)K}{-3+(2/5)K}\]
but if that denominator is zero, this x doesn't exist and so we have no solutions. Then set this equal to zero:
-3+(2/5)K = 0
(2/5)K = 3
K = 15/2 = 7.5
I'm not sure where 35/2 is coming from, especially since if K = 35/2, if x = 71/8 and y = -7/4, the equations work out so it has a solution.

Answer 12

ok dear

Answer 13

thank for ur help

Answer 14

You're welcome! I hope it makes some sense now.

Answer 15

it is hard, is it?

Answer 16

its result is 15/2

Answer 17

am sorry

Answer 18

The answer should be 15/2, yes.

Answer 19

so do the same step like you did?

Answer 20

Yep. Basically, proceed like K is a number and you're solving to find the solution, but at some point, we have to ask "Wait, what if K was this number?" which is what happened when I divided and had a K in the denominator.

Answer 21

it is just a number like x and y

Answer 22

Right.

Answer 23

can i ask you other math?

Answer 24

Sure!

Answer 25

If f(x) and g(x) are two functions defined by


f(x) = √(x + 1)
g(x) = | x - 1 |,

then what is the value of f(g(9))?

Answer 26

"f(g(9))" means plug 9 in for x in g(x), and then take that answer and plug it in to x in f(x). So:
g(9) = |9-1| = |8| = 8.
Plug in to f(x):
f(g(9)) = f(8) = √(8 + 1) = √(9) = 3.

Answer 27

yes it is thank you