Simultaneous Quadratic Equations

1
Simultaneous Quadratic Equations
2
Graphically

• Solve
• x2 5x y 0
• and
• x y 3

xy3
x25xy0
There are TWO solutions
x-3 and y6 OR x-1 and y4
3
Algebraically

• Solve
• x2 5x y 0
• and
• x y 3

? x2 5x 3 x 0
? x2 4x 3 0
? y 3 - x
? If x-3, then y 6
? If x-1, then y 4
? (x3)(x1) 0
? x-3 OR x-1
4
Graphically

• Solve
• x2 y2 8
• and
• x y 4

xy4
x2y20
There is only ONE solution
x2 and y2
5
Algebraically
? x2 (4-x)2 8

• Solve
• x2 y2 8
• and
• x y 4

? x2 16 8x x2 8
? 2x2 8x 16 -8 0
? x2 4x 4 0
? y 4 - x
? If x2, then y 2
? (x-2)2 0
? x 2
6
Graphically

• Solve
• x2 2x y
• and
• y 0.5x -3

x2 2x y
y 0.5x -3
There are NO solutions
7
Algebraically

• Solve
• x2 2x y
• and
• y 0.5x -3

? x2 2x -3 -0.5x
? x2 2.5x 3 0
? y -3 0.5x
? No solutions