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Can you solve the following 2 simultaneous equations; y=6x-2 and x^2-4x+19=y?

y=6x-2

x2-4x+19

Both equations are equal to Y, hence can be substituted into each other;

6x-2= x^2-4x+19

Now we only have X terms in our equations

Bring all the like X terms together, and make equation equal to 0

  1. 6x-2= x^2-4x+19
  2. 6x= x^2-4x+19+2
  3. 6x= x^2-4x+21
  4. 0= x^2-4x+21-6x
  5. 0= x^2-10x+21

Now we have a simultaneous equations which we can factorise

0=(x-7)(x-3)

We can now solve this as either x-7 must equal 0 or x-3 must equal 0

0=x-7………………………………x=7

Or

0=x-3………………………………x=3

Hence answer is x=7 or 3

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