I have this simultaneous equation: \(\begin{cases}x^2-4x+4+y^2-2y+1=9\\x^2-10x+25+y^2-14y+49=36\end{cases}\) How do I solve

Leroy Davidson

Leroy Davidson

Answered question

2022-03-30

I have this simultaneous equation:
{x24x+4+y22y+1=9x210x+25+y214y+49=36
How do I solve it?

Answer & Explanation

Ireland Vaughan

Ireland Vaughan

Beginner2022-03-31Added 14 answers

Step 1
To start with, notice that we can rewrite the given system as:
{(x2)2+(y1)2=9 (x5)2+(y7)2=36 
Besides this, you can subtract the first equation from the second in order to obtain:
(x210x+25+y214y+49)(x24x+4+y22y+1)=369
whence get that
6x+2112y+48=276x12y=42
x+2y=7
Then you can apply such relation into any of the equations above.

Riya Erickson

Riya Erickson

Beginner2022-04-01Added 12 answers

Substract both equations to obtain a linear equation in two variables. Rearrange it to write one variable in terms of the other, replace that expression in one of the original quadratic equations, to then solve a quadratic equation in one variable.

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