Question

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

Answer 1

first, you can multiply the first equation by -3.
That eliminates x. That is the type of elimination you're working on, right?

Answer 2

yes I think so. I have never used elimination method before so this is new to me.

Answer 3

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?

Answer 4

Yes. It is still vague but I am grasping it.

Answer 5

anything need further explanation?

Answer 6

No. Thank you so much for all your help!!

Answer 7

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.

Answer 8

* x's equal and opposite, so they cancel.

for this one, but for a different problem, it might be simplest to eliminate the y

Answer 9

next, we find the x value. do you know how to substitute y into one of the original equations and solve for x ?

Answer 10

No. I am terrible at this. Farthest I know is basics.

Answer 11

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.

Answer 12

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. :)

Answer 13

Wow! thank you! I appreciate that greatly! Thank you!

Answer 14

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.
:)