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3.2 Solving Systems Algebraically
Solving System AlgebraicallySubstitution
y = 2x + 5x = -y + 14
Solving System AlgebraicallySubstitution
y = 4x – 7y = ½ x + 7
Solving System AlgebraicallyElimination
x + 6y = 102x + 5y = 6
Solving System AlgebraicallyElimination
2x + 5y = -13x + 4y = -5
When to use substitution?
1) A variable in an equation is isolated
2) Both equations are in y = mx +b form
When to use elimination?
1) Equations are in standard form
ax + by = c
Special Case #1
x + 3y = 102x + 6y = 19
The solution to they system is false because 0 = -1.
There is no solution because the lines are parallel.
Special Case #2
2x – 5y = 8-4x + 10y = -16
The solution to they system is always true because 0 = 0.
There is an infinite number of solutions is because they are the same line.
Parametric Equations
• Parametric Equations are equations that express the coordinates of x and y as separate functions of a common third variable, called the parameter.
•You can use parametric equations to determine the position of an object over time.
Parametric Example
• Starting from a birdbath 3 feet above the ground, a bird takes flight. Let t equal time in seconds, x equal horizontal distance in feet, and y equal vertical distance in feet. The equation x(t)= 5t and y(t)=8t+3 model the bird’s distance from the base of the birdbath. Using a graphing calculator, describe the position of the bird at time t=3.