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simultaneous equation i need help with watch

1. x+2y=3
x^2-2y+4y^2=18

the textbook says the answers are x =1.5, y=2.25; x=4, y =-0.5 but i've tried all ways I know used up 4 pages and haven't gotten any of the right answers so any help would be greatly appreciated
2. (Original post by Jsv1997)
x+2y=3
x^2-2y+4y^2=18

the textbook says the answers are x =1.5, y=2.25; x=4, y =-0.5 but i've tried all ways I know used up 4 pages and haven't gotten any of the right answers so any help would be greatly appreciated
Rearrange equation 1 to find x in terms of y.

Substitute x in terms of y into equation 2, then solve the quadratic for y.

Substitute the values of y into equation 1 to find x.

Done.
3. Might sound really advanced lol or long but here it is:
Substitute x from the first equation Into the second by rearranging the equation.

X = y - 2x
Substitute x into the second equation.
Let's see how you do from there, if you need further help, just reply back and I'm ready to help.
There are 2 ways to get to both of hype answers and I've got both of them but I can't give the full answer 😀 so this is a starter.

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4. could try altering the lnear equation to read:

sub this into the equation for the ellipse, and simplify (expand).

You should get:

which can be factorised...
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5. (Original post by Jsv1997)
x+2y=3
x^2-2y+4y^2=18

the textbook says the answers are x =1.5, y=2.25; x=4, y =-0.5 but i've tried all ways I know used up 4 pages and haven't gotten any of the right answers so any help would be greatly appreciated
You can write the second equation as . And then you know and you can also rearrange this to get and substitute that in.
6. (Original post by Hasufel)
could try altering the lnear equation to read:

sub this into the equation for the ellipse, and simplify (expand).

You should get:

which can be factorised...
That is too much lol, the answer is obvious now. But meh... I was gonna do that too

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7. (Original post by Jsv1997)
x+2y=3
x^2-2y+4y^2=18

the textbook says the answers are x =1.5, y=2.25; x=4, y =-0.5 but i've tried all ways I know used up 4 pages and haven't gotten any of the right answers so any help would be greatly appreciated
thanks for all the help I checked it over it turns out I had the numbers wrong after factorizing I had (4x+1)(2x-9) instead of (4x-9)(2x-1) but thanks for all the help anyway
8. (Original post by Jsv1997)
thanks for all the help I checked it over it turns out I had the numbers wrong after factorizing I had (4x+1)(2x-9) instead of (4x-9)(2x-1) but thanks for all the help anyway
Now that you understood how to get the answer, I'll show you the other way I was talking about, a bit weird lol but yeh.

First of all, substitute the 1st linear equation into the next equation.

x = 2y - 3
Therefore, x^2 - 2y + 4y^2 = 18 becomes (3-2y)^2 - 2y + 4y^2 = 18.

This is now 9-6y-6y+4y^2-2y+4y^2 = 18
Simplify it > 9 - 12y + 4y^2 - 2y + 4y^2 = 18
Then, 8y^2 - 14y + 9 = 18
8y^2 - 14y = 9
Factorise it, 2y(4y - 7) = 9
Therefore, 2y(4y) = 2
8y^2 = 2
Divide both sides by 8 to get y^2.
y^2 = 2/8 = 0.25 or 1/4
Square root both sides
y = square root of 0.25 = 0.5

I don't know how to get to -0.5 though lel. Maybe it's this:

2y(4y - 7) = 9
Therefore, 2y(4y) = 9 + 7 = 16
8y^2 = 16
Square root both sides, 8y = -4 or 4, i choose -4.
-4 / 8 = -0.5

Or you can use the quadratic formula and get the answers, much faster and easier .

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