+0

# Solve the system

0
235
4
+88

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
+81154
+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
Sort:

#1
+91513
+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
+889
+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
+81154
+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
#4
+91513
0

Thanks guys,

sometimes it pays to finish a question.

I suppose it also pays to look at a question sensibly before plowing headlong into the algebra   :)

Melody  Mar 25, 2015

### 10 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details