Three variable equation solving.?

Question

I am trying to complete a pre-calculus study guide. I know how to solve for two variable system of equations, but having difficulty solving this one. It's also saying to find the value of d without having a solution... maybe i'm not reading it correctly, but it seems like they want a value for d with all the other variables unsolved????

Find the value of such that the system of equations

6x + dy = -20

4x + 10y = 19

does not have a solution.

Answer 1

The two equations are two lines on the xy graph.

There would not have solution,

if they DO NOT intersect.  So what is the value of d ??

there is not necessary to find any x or y.

Answer 2

idk thats hard

Answer 3

ummm what the h**l does that mean????

Answer 4

The most likely answer is that the 'dy' is a typo.  If it is actually mean to be dy as in 'change in y', then dy evaluates to zero in this case, then x = -3.333 and y = -0.5667

Answer 5

it means the lines need to be parallel, so you need a d where the lines are parallel. in other words the coefficients before x and y need to have the same ratio in both equations.

6/d=4/10

then cross multiply...

60=4d

d=15

make it a good day

Answer 6

Just ignore the D for awhile and imagine it was just another number.  Then try to eliminate a variable.  For example, if you double the first equation and triple the second, you'll be able to eliminate x.

12x + 2dy = -40

12x + 30y = 38

Subtract the first equation from the second:

30y - 2dy = 38 - (-40)

(30 - 2d)y = 78

y = 78/(30 - 2d)

Now notice... most values that you put in for d will result in a value for y.  But what if you made the denominator come out as zero?  That would lead to no solutions because division by zero is not allowed.

30 - 2d = 0

2d = 30

d = 30/2

d = 15

To double-check, imagine that d = 15 and try solving the two equations.  You'll get to an inconsistency and thus no solution.

6x + 15y = -20

4x + 10y = 19

12x + 30y = -40

12x + 30y = 57

0 = 97*

Value of (d = 15) results in no solutions

Answer:

d = 15