We have
Equation 1
x2 + y2 = 34
Equation 2
(x - 7)2 + y2 = 41
We can multiply Equation 1 by negative 1 and add it to Equation 2
-x2 - y2 = -34
(x -7)2 + y2 = 41
y2 is obviously eliminated but so is x2 we have
-x2 + (x -7)2 = 7
Expand (x -7)2
-x2 + x2 -14x + 49 = 7
The x2's cancel out, then we combine like terms on both sides of the equal sign to give
-14x = 7 - 49
-14x = -42
Divide both sides by -14 to give
x = 3
To solve for y we can plug x = 3 into original Equation 1
32 + y2 = 34
9 + y2 = 34
Subtract 9 from both sides of the equation
y2 = 25
y = √25
y = 5
Checking
(x - 7)2 + y2 = 41
(3 - 7)2 + 52 = 41
(-4)2 + 25 = 41
16 + 25 = 41
41 = 41
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