x^2+y^2=4

x+y=2

**Type your answer as ordered pairs (x,y) with the order: from the smallest value of x to the largest, with comma and no space.**

zandaleebailey
Mar 24, 2015

#3**+10 **

x^2+y^2=4

x+y=2

This is the intersecction of a line and a circle

Using the second equation we can write y = 2 - x

And substituting this into the first equation for y, we have

x^2 + (2 - x)^2 = 4 simplify

x^2 + x^2 - 4x + 4 = 4 subtract 4 from both sides and simplify

2x^2 - 4x = 0 factor

2x(x - 2) = 0 setting each factor to 0, we have that x = 0, and x = 2

And using x + y = 2

When x = 0, y = 2

When x = 2, y =0 so the answers are (0,2) (2,0)

Here's a graph......https://www.desmos.com/calculator/eakj6g1q0t

CPhill
Mar 24, 2015

#1**+5 **

$$\\x^2+y^2=4\qquad(1)\\\\

x+y=2 \;\;\rightarrow \;\;y=2-x\qquad(2)\\\\

sub\;\;2\;into\;1\\\\

x^2+(2-x)^2=4\\\\

x^2+4+x^2-4x=4\\\\

2x^2-4x=0\\\\

2(x-2)(x+2)=0\\\\

x=\pm 2$$

You can find the y values :)

Melody
Mar 24, 2015

#2**+10 **

x = 2 implying y = 0 is ok. but x = -2 leads to a contradiction.

Also, the equations are symmetric in x and y, so it's possible to switch the x and y values to obtain a second solution corresponding to x=2, y=0.

An alternative method of solution would be to square the second equation and then combine that with the first leading to 2xy = 0, from which either x = 0, or y = 0.

Then substitute into the second equation, (not the first), to find the corresponding y or x value.

Bertie
Mar 24, 2015

#3**+10 **

Best Answer

x^2+y^2=4

x+y=2

This is the intersecction of a line and a circle

Using the second equation we can write y = 2 - x

And substituting this into the first equation for y, we have

x^2 + (2 - x)^2 = 4 simplify

x^2 + x^2 - 4x + 4 = 4 subtract 4 from both sides and simplify

2x^2 - 4x = 0 factor

2x(x - 2) = 0 setting each factor to 0, we have that x = 0, and x = 2

And using x + y = 2

When x = 0, y = 2

When x = 2, y =0 so the answers are (0,2) (2,0)

Here's a graph......https://www.desmos.com/calculator/eakj6g1q0t

CPhill
Mar 24, 2015