Question

In the system of equations below, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?

\(kx-3y=4\\4x-5y=7\)

A) \(\dfrac{12}{5}\)

B) \(\dfrac{16}{7}\)

C) \(-\dfrac{16}{7}\)

D) \(-\dfrac{12}{5}\)

Answer 1

`t` suppose to be y ?? right?

Answer 2

ye

Answer 3

in order to get no solution, the coefficients of both variables should be the same but opposite sign.

like in this example
\[\large\rm 3x -4y=9\]\[\large\rm -3x+4y=7\]
3x cancels out same with y variable
left with 0=16

Answer 4

so first i would try to get same coefficients for y variable.
then it would be easy to find k

Answer 5

how would I do that?

Answer 6

multiply first equation by 5 and equation by -3

Answer 7

2nd e quation by -3*

Answer 8

\(5(kx-3y=4)\)

I multiply k by 5 too or no?

Answer 9

yes multiply all terms by 5

Answer 10

\(5kx-15y=20\)

\(-12x+15y=-21\)

Answer 11

looks good to me
now you can try each option to find value for k

\(\rm 5kx-15y=20\)
\(\color{Red}{-12x}+15y=-21\)
remember our goal is to cancel out both variables
so which option will give you 12 when you multiply by 5 ??

Answer 12

D?

Answer 13

\[\rm 5(\frac{-12}{5})x-15y\]
you will get \[\large\rm -12x -15y=20\]
and the 2nd e quation is
\[\large\rm -12x -15y=20\]\[\large\rm -12x+15y=-21\]
would you get no solution ?

Answer 14

there is one solution

Answer 15

yes try other option
\[\large\rm -12x \cancel{-15y}=20\]\[\large\rm -12x\cancel{+15y}=-21\]
like i said the sign should be opposite
-12x-12x is not equal to 0

Answer 16

try A?

Answer 17

try it
do you get 0 ??

Answer 18

did you substitute k for option A ??

Answer 19

\(5(\dfrac{12}{5}x-15y=20\\12x-15=20\)
?

Answer 20

yes that's correct now what's the 2nd equation ?
and i guess there is a typo you forgot the y variable

Answer 21

\(12x-15y=20\\-12x+15y=-21\)

Answer 22

right solve it

Answer 23

0 = -1 ?

Answer 24

right so that means no solution.

Answer 25

so A is my answer then?

Answer 26

thats what we get so yes

Answer 27

oke
ty ^_^

Answer 28

yw