At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
first, you can multiply the first equation by -3. That eliminates x. That is the type of elimination you're working on, right?
yes I think so. I have never used elimination method before so this is new to me.
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?
Yes. It is still vague but I am grasping it.
anything need further explanation?
No. Thank you so much for all your help!!
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.
* x's equal and opposite, so they cancel. for this one, but for a different problem, it might be simplest to eliminate the y
next, we find the x value. do you know how to substitute y into one of the original equations and solve for x ?
No. I am terrible at this. Farthest I know is basics.
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.
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. :)
Wow! thank you! I appreciate that greatly! Thank you!
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. :)