Solve a quadratic system by elimination

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EXAMPLE 3
Solve a quadratic system by elimination
Solve the system by elimination.
9x2 y2 90x 216 0
Equation 1
x2 y2 16 0
Equation 2
SOLUTION
9x2 y2 90x 216 0
10x2 90x 200 0
Add.
x2 9x 20 0
Divide each side by 10.
(x 4)(x 5) 0
Factor
x 4 or x 5
Zero product property
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EXAMPLE 3
Solve a quadratic system by elimination
When x 4, y 0. When x 5, y 3.
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EXAMPLE 4
Solve a real-life quadratic system
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EXAMPLE 4
Solve a real-life quadratic system
x2 y2 16x 32 0
Equation 1
x2 y2 8y 8 0
Equation 2
SOLUTION
x2 y2 16x 32 0
16x 8y 40 0
Add.
y 2x 5
Solve for y.
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EXAMPLE 4
Solve a real-life quadratic system
x2 y2 16x 32 0
Equation 1
x2 (?2x 5)2 16x 32 0
Substitute for y.
3x2 4x 7 0
Simplify.
(x 1)(3x 7) 0
Factor.
Zero product property
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EXAMPLE 4
Solve a real-life quadratic system
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for Examples 3 and 4
GUIDED PRACTICE
Solve the system.
7.
2y2 x 2 0
x2 y2 1 0
(0, 1) , ( , )
ANSWER
8.
x2 y2 16x 39 0
x2 y2 9 0
(3, 0) , (5, 4)
ANSWER
8
for Examples 3 and 4
GUIDED PRACTICE
Solve the system.
9.
x2 4y2 4x 8y 8
y2 x 2y 5
ANSWER
(6, 1), (2, 3), (2, 1).
9
for Examples 3 and 4
GUIDED PRACTICE
x2 y2 12x 18 0
Equation 1
y2 x2 4y 2 0
Equation 2
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,
ANSWER