Help simultaneous equations question

iamspiderman

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(edited 7 years ago)

Reply 1

Zacken

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Original post by iamspiderman

Solve the simultaneous equations:

Y= 2x - 3
X^2 + y^2 = 2

You have two equations, substitute the first one into the second and see what you get? :smile:

Reply 2

iamspiderman

OP

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(edited 7 years ago)

Reply 3

Zacken

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Original post by iamspiderman

Ok I did that:

X^2 + (2x -3)= 2

You need to square the (2x-3), this then forms a quadratic expression, so why don't equate it to zero, that is subtract 2 from both sides and then factorise/solve using the quadratic formula to get the two values of x? You can then sub these two values of x to get two values of y? :smile:

(edited 9 years ago)

Reply 4

Lauren2812

12

When you substitute it in you need to remember it is still squared. So it will be(2x -3)^2. That is the same as (2x -3)(2x-3) and you then need to expand that. Then collect all like terms (remembering the other x^2) and then make it equal to zero and then factorise that. T

Reply 5

iamspiderman

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(edited 7 years ago)

Reply 6

Zacken

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Original post by iamspiderman

Thanks for replying!

Ok I've got : x^2 + (2x-3) (2x-3) = 2
And I need help expanding and factorising. Maths is not my strongest of subjects. :smile:

To expand brackets of the form

(a+b)(a+b)

, it can be written like this:

(a \times a) + (a \times b) + (a \times b) + (b \times b)

, which can then be shortened to:

a^2 + 2ab + b^2

.

So when you have a bracket of

(2x-3)(2x-3)

, you'd expand it like:

(2x \times 2x) + (2x \times -3) + (2x \times -3) + (-3 \times -3)

which can be written as:

4x^2 - 12x + 9

, so you can now write your original equation as:

x^2 + 4x^2 - 12x + 9 = 2

, if there's something you don't understand, tell me and I'll try to clear it up. :smile:

(edited 9 years ago)

Reply 7

Lauren2812

12

So, expanding (2x-3)(2x-3)...
Do you use foil? First, outer, inner, last?
First 2x x 2x = 4x^2
Outer 2x x -3 = -6x (plus and a minus makes a minus)
Inner -3 x 2x = -6x
Last -3 x -3 = 9 (a minus and a minus make a plus)

So now you've got x^2 + 4x^2 -6x -6x + 9 = 2
Subtract two off both sides so it equals zero.
Now collect all like terms (x's together, x^2's together, integers together etc.)
Then you factorise what you've got.
Then you can work out what x equals and then use them to substitute into the first equation to find out what y equals.
And if you need anymore help I'll help later, gotta go to college now. Have a nice day. :smile:

Reply 8

iamspiderman

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(edited 7 years ago)

Reply 9

Zacken

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