Im stumped on a math question... help!?

Question

Find the value of c such that the system of equations does not have a solution

-6x + 9y = -7
10x + cy = -14

***What?! that doesnt make any sense to me!?**

Answer 1

If c is some unknown number, the solutions to this system of equations will be different for different values of c. For one particular value of c there will be no solutions at all; you have to find that value of c.

Since c doesn't appear in the x terms, we can eliminate x fairly easily: add 5 times the first equation to 3 times the second to get
-30x + 30x + 45y + 3cy = -35 + (-42)
<=> (45 + 3c) y = -77
<=> y = -77 / (45 + 3c) as long as 45 + 3c ≠ 0.
So if c ≠ -15 there is a solution for y, and hence for x by substituting this value in. But if c = -15 we have
(45 + 3c) y = -77
<=> 0 = -77
which has no solution.

So there are no solutions iff c = -15.

Answer 2

it simply means that the two equations do not have a definite solution. I hope you know what b^2-4ac means.

-6x + 9y = -7 -------(1)
10x + cy = -14-----(2)

From (1):
x= (7+9y)/6------(3)

From (2):
x = (-14-cy)/10 -------(4)

substitute (3) into (4):
(7+9y)/6 = (-14-cy)/10

70 + 90y = -84 -6cy
90y+6cy= -154
90y+6cy+154=0
(90+6c)y+154=0 -------(5)

Now, there is no solution for (5) only when b^2-4ac<0.

So,
(90+6c)^2 -4*0*154<0
(90+6c)(90+6c)<0

solve, and you will get the answer: c=-15.

Answer 3

There will be no solution if the lines are parallel.
-6x + 9y = -7 <-- Eq1
10x + cy = -14 <-- Eq2
Eq 1 can be rewritten as :
y=6x/9 -7/9 --> slope = 2/3
Eq2 can be rewritten as:
y=-10x/c -14/c --> slope = -10/c
So to make slopes the same we have:
-10/c=2/3
2c=-30
c= -15
When c = -15, the lines are ||, and so no solution.

Answer 4

initiate by making use of dispensing the three into the x-4. To distribute, you're taking the selection on the exterior of the parentheses (3) and multiply it by making use of the separate values on the interior (x) (-4). three times x equals 3x. three times -4 is -12. combine the values. you at the instant are left with 3x-12. Your equation now sounds like this: x + 8 = 3x - 12 Now you may desire to get each and all the x values on the comparable edge: x + 8 = 3x - 12 -1x -1x 8 = 2x - 12 (From right here i anticipate you recognize a thank you to remedy it, yet nonetheless) +12 + 12 20 = 2x /2 /2 10=x properly, this is the respond. Sorry if I at a loss for words you.

Answer 5

c= -15