6-1 Graphing Systems of Equations

N#_____ ____/____/____

System of equations – two or more equations

• Solution is an ordered pair that satisfies all equations.

• Where the lines intersect

• There can be 0, 1, or an infinite number of solutions.

Intersecting Lines

Same Line

Parallel Lines

One Solution

Consistent (intersecting)

Independent (one solution)

Infinitely

many

solutions

Consistent

(intersecting)

Dependent

(more than

one solution)

No solutions

Inconsistent

(do not intersect)

x

y

x

y

Ex 1Which system has no solution, one solution or infinitely many solutions.

x

y

Ex 2 Solve the system of equations.

2x – y = -3

8x – 4y = -12

x

y

Ex 3 Solve the system of equations.

x – 2y = 4

x – 2y = -12

x

y

Ex 4 Solve the system of equations.

y = -x + 8

y = 4x - 7x

y

A#____ ____/____/____ PWS 6-1 #’s 1-7