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3.2 Solving Systems Algebraically. Solving System Algebraically Substitution. y = 2x + 5 x = -y + 14. Solving System Algebraically Substitution. y = 4x – 7 y = ½ x + 7. Solving System Algebraically Elimination. x + 6y = 10 2x + 5y = 6. Solving System Algebraically Elimination.

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## 3.2 Solving Systems Algebraically

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**Solving System AlgebraicallySubstitution**y = 2x + 5 x = -y + 14**Solving System AlgebraicallySubstitution**y = 4x – 7 y = ½ x + 7**Solving System AlgebraicallyElimination**x + 6y = 10 2x + 5y = 6**Solving System AlgebraicallyElimination**2x + 5y = -1 3x + 4y = -5**When to use substitution?**A variable in an equation is isolated Both equations are in y = mx +b form**When to use elimination?**Equations are in standard form ax + by = c**Special Case #1**x + 3y = 10 2x + 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.

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