Solve the simultaneous equations x y 8 and x 2 ... - SS2 Mathematics Simultaneous Linear and Quadratic Equations Question
Solve the simultaneous equations \(x + y = 8\) and \(x^{2} - y^{2} = 16\).
A
(0; - 3) or ( - 7;5)
B
( - 4;3) or (2;5)
C
(5;3)
D
(3;3) or (5;5)
correct option: c
\(x + y = 8\) (1)
\(x^{2} - y^{2} = 16\) (2)
From (1), transpose \(y\)
\[x + y = 8\]
\[y = 8 - x\]
Substitute the value of \(y\) in (2)
\[x^{2} - {(8 - x)}^{2} = 16\]
\[16x - 64 = 16\]
\[16x = 16 + 64\]
\[16x = 80\]
\[16x - 80 = 0\]
\[16(x - 5) = 0\]
\[\therefore x = 5\]
Substitute the values of \(x\) in (1)
\[x + y = 8\]
\[5 + y = 8\]
\[y = 8 - 5 = 3\]
The solution to the simultaneous equations \(2x + y = 5\) and \(x^{2} + y^{2} = 25\) is the ordered pairs: \((5;3)\)
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