anonymous
  • anonymous
Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. 8x + 10y = 92 24x + 11y = 162
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mysesshou
  • mysesshou
first, you can multiply the first equation by -3. That eliminates x. That is the type of elimination you're working on, right?
anonymous
  • anonymous
yes I think so. I have never used elimination method before so this is new to me.
mysesshou
  • mysesshou
ok, both sides, multiply by -3 -3 * (8x + 10y )= (92) * -3 gives -24x -30y = -276 (eq1) add this to the other equation, eq2: -24x -30y = -276 (eq1) + 24x + 11y = 162 (eq2) the x's cancel because -24x+24x = 0 -18y = -114 y = 19/3 ok so far?

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anonymous
  • anonymous
Yes. It is still vague but I am grasping it.
mysesshou
  • mysesshou
anything need further explanation?
anonymous
  • anonymous
No. Thank you so much for all your help!!
mysesshou
  • mysesshou
What we're doing is setting the x's equal, so then we solve for the y that fits both equations. then when we find y, we can substitute it back into an original equation and find the x.
mysesshou
  • mysesshou
* x's equal and opposite, so they cancel. for this one, but for a different problem, it might be simplest to eliminate the y
mysesshou
  • mysesshou
next, we find the x value. do you know how to substitute y into one of the original equations and solve for x ?
anonymous
  • anonymous
No. I am terrible at this. Farthest I know is basics.
mysesshou
  • mysesshou
ok, let's take the original equation: 8x + 10y = 92 if y = 19/3, then we replace the y with that number. 8x + 10*(19/3) = 92 and solve for the x.
mysesshou
  • mysesshou
8x + 10*(19/3) = 92 simplify to: 8x + (190/3) = 92 subtract (190/3) from both sides: 8x = 92 - (190/3) simplify: 8x = (86/3) divide both sides by the 8 to get x alone: x = (86/3)/8 = x = 43/12 so your solution is ( 43/12 , 19/3 ) but let's make sure I typed all this correctly, as typing isn't as simple as writing :) Take an original equation 8x + 10y = 92 plug in the values for x and y, see if it works. 8(43/12) + 10(19/3) = 92 86/3 + 190/3 = 92 True, so they worked properly. :)
anonymous
  • anonymous
Wow! thank you! I appreciate that greatly! Thank you!
mysesshou
  • mysesshou
you're welcome :) Hope the process helps you figure out others, if not, there are people here to help :) It is always good to check your work, like I did at the end, to make sure you didn't make a mistake. Also, to start off, you look at the two equations, what is similar that it could just be multiplied by something and they would cancel? That is how I picked the x to eliminate, since by multiplying the first equation by -3, then it became -24x. good luck. :)

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