Solving eqnt with infinite solutions

[Apphysics]

Hello,

i have a problem that states for what value(s) would make the system kx-5y=8 and 7x +5y=10. When I try to solve for one variable and plug it into the second equation it doesnt give me a number solution, it gives me a solution with a variable. The variables don't cancel out. Can you please help. Thanks

 

[mmm4444bot]

for what value(s) would make the system kx-5y=8 and 7x +5y=10

Are they asking for value(s) of k that make the system consistent? (Seems like there's words missing, above.)

Also, please read the forum guidelines; here's a link to the summary page.

Thank you :cool:

 

[HallsofIvy]

Hello,

i have a problem that states for what value(s) would make the system kx-5y=8 and 7x +5y=10.

Would make the system what? You have left something out!

 

[Apphysics]

Yes, the value or values for k that makes the system with infinite solutions. I couldn't find the value for k because the value of k includes a variable. Thanks for the help

 

[stapel]

Yes, the value or values for k that makes the system with infinite solutions. I couldn't find the value for k because the value of k includes a variable. Thanks for the help

What do you mean by the variable "k" "including" a variable?

What is the form of the solution for a system of equations where the solution set is infinite? When you go to solve that sort of system, what sort of solution format do you get? For instance, when you solve a system with no solution, you end up with an equation that's nonsense, like "2 = 3". But what's the form when the solution is infinite?

Do the computations to eliminate one or the other of the "regular" variables (being x and y). Then use what you know about the form of an "infinite solution" system to figure out a value for k.

If you get stuck, please reply showing your efforts so far. For instance, another poster replied with the beginning of an "addition method" solution. Where did you go from there? Thank you!

 

[HallsofIvy]

We can't "guess" what/how you're doing...
You have these 2 equations:
kx - 5y = 8 [1]
7x + 5y = 10 [2]

Add them:
kx + 7x = 18
So:
x(k + 7) = 18
x = 18 / (k + 7)

What's the next step? SHOW IT, please.

This is what Denis showed you from the start. Now the problem is to solve for x and y: k is a "given" number so you (or rather Denis) has already solved for x unless k is a specific number. For what value of k does x= 18/(k+ 7) NOT give a solution for x?