MOST can’t solve this ALGEBRA Equation!

[@tomtke7351]

To start, there's 2 unknowns: X and Y And there's two equations: X^2+Y^2 = 8 eq.1 X = (1/2)Y+1 eq.2 AND SINCE THERE'S ^2 power means there's two solutions to simplify: 2X = Y + 2 eq.2.1 Y = 2X - 2 eq.2.2 eq.2.2 into eq.1 X^2 +[2X-2]^2 = 8 eq.1.1 X^2 +4X^2 -8X +4 = 8 5X^2-8X - 4 = 0 eq1.2 quad equation: [-b +/- sqrt(b^2-4ac)]÷2a a = 5 b = -8 c = -4 [8 +/-sqrt(64+80)]÷10 [8+/-sqrt(144)]÷10 [8+/-(12)]÷10 20/10, -4/10 X.1 = 2 X.2 = -0.4 Y = 2X - 2 eq.2.2 Y.1 = 2(2)-2 = 2 Y.2 = 2(-0.4)-2 = -2.8 VERIFY: X.1, Y.1 = (2,2) X.2, Y.2 = (-0.4, -2.8) c X^2+Y^2 = 8 eq.1 2^2+2^2 = ? 8 4 + 4 =❤ 8✔️ (-0.4)^2 + (-2.8)^2 =? 8 0.16 + 7.84 =?8 8 =❤ 8✔️ FINAL ANSWER: X.1, Y.1 = (2,2) X.2, Y.2 = (-0.4, -2.8) COMMENT: X^2+Y^2 = 8 is a circle. X = (1/2)Y + 1 is a straight line the straight line intersects the circle in two places.

[@PaulBusuttil-z4x]

This problem encompasses many algebraic equations to solve. And only got as far as (2,2). However John’s explanation made it look straightforward, as he usually does. One aspect I didn’t understand however is the stand alone X in the calculation; x2 +1/4x2+x+1=8. Otherwise enjoying John’s videos and comments in general. Paul

[@devonwilson5776]

Greetings. The answers are (2,2) and (+,-14/5, -2/5). Based on the expressions given, using equation 2 gives X =2Y-2 We will now substitute this value of X in equation 1 to get (2Y-2)^2 +Y^2=8 and 4Y^2-8Y+4+Y^2=8, (4Y^2+Y^2)-8Y +4-8=0, 5Y^2-8Y-4=0, (5Y+2)(Y-2)=0. Now, setting (5Y+2)=0, and (Y-2)=0, we have Y=2, -2/5. We shall now substitute these values of Y in equation 2 and by doing so it is determined that X equals 2, -14/5. However, I have also determined that X equals 14/5 if -2/5 is substituted in equation 1. Therefore, when Y=-2/5, X=-14/5 or 14/5.

[@garystrittmater8258]

Substitute y=1/2x +1 into y squared, solve for x, find x and substite back to find y!

[@russelllomando8460]

good one. very involved. thanks for the explanation.

[@kevinreist7718]

x= 2 and y = 2. I solved this in my head. Now, I'll watch to see if he has some other surprise for us. I didn't forsee 2 negative fractions being squared as another possible solution. Oh well, can't say that I even care about a second possible solution.

[@MrMousley]

Looking at the first one I just thought that it would work if X and Y were both 2 2 squared + 2 squared = 4 + 4 = 8 and then, looking at the second one, I realised that that worked as well Y = 1/2 X + 1 2 = 1/2(2) + 1 2 = 1 + 1

[@chadsoltys4127]

That's wut I did, took about 6 seconds.

[@rydmerlin]

Why when you factored this did you write the factors in different order? Isn’t it more logical to read it as (5x + 14) (x - 2)

[@paulettepaulsen2336]

I decided x=2 and y=2, but if the numbers were larger I wouldn't know how to go through all those steps.

[@wilheminaoppong6527]

Thank you very much SIr

[@genelowry5666]

Thank you, after 60+ years I’m enjoying the review.

[@mollymam7153]

I better double check when x= -14/5

[@Charisse0623]

Where’d the x come from in x^2+1/4x^2+x+1?

[@vespa2860]

Bit late, but foil out (1/2X + 1) (1/2X + 1) gives 1/4X^2 + 1/2X+ 1/2X +1 Which simplifies to 1/4X^2 + X +1 John cut out this part to the simplified answer for some brevity.

[@mollymam7153]

y= -2/5, of course

[@danielmadden9691]

I struggled with this one

[@mortamustyler8166]

X^2+y^2=8.....why did he decide that y =1/2x+1??? How is not x=2.5 y=1.5?

[@danielmadden9691]

X=√5&8/9,Y=√3&8/9

[@danielmadden9691]

I forgot about the circle equation, been out of school since late70's

[@danielmadden9691]

I also forgot x can=y

[@rajalakshmik6148]

X=2,_2,8 Y=2,_0.4

[@gillianrolland4305]

I loved Maths at school but Id hated it if you'd been my teacher. Too many words and irrelavancies

[@Vokyavokya]

You are not teach in details this way

[@afre3398]

I do not agree. This is a valid algebra problem By any means At least this time. I know this youtuber has a track record of ambiguity