3.2 solving systems algebraically. solving system algebraically substitution y = 2x + 5 x = -y + 14

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.