Solve Systems of Equations By

Graphing

VOCABULARY

• A system of two linear equations, also called a linear system, in two variables x and y consists of two equations that can be written in the following form:

Ax + By = C

Dx + Ey = F

VOCABULARY• A solution of a system of linear

equations in two variables is an ordered pair (x, y) that satisfies both equations. – At least 1 solution: CONSISTENT– No solutions: INCONSISTENT [graph

is parallel lines] – Exactly 1 solution: INDEPENDENT– Infinitely many solutions:

DEPENDENT

VOCABULARY• CONSISTENT INDEPENDENT

• CONSISTENT DEPENDENT

• INCONSISTENT

EXAMPLES

1) Check whether the ordered pair is a solution of the systems.

a. (7, 4) y + x = 11 y – 2x = -10

EXAMPLES

1) Check whether the ordered pair is a solution of the systems.

b. (1, 5) 3x - 2y = 7 y = 2x + 1

EXAMPLES2) Graph the linear system and estimate the

solution. Then check the solution algebraically.

a. y = –3x + 5 y = 2x – 5

EXAMPLES2) Graph the linear system and estimate the

solution. Then check the solution algebraically.

b. 3x + y = 7 y = 2x - 3

EXAMPLES3) Graph the linear systems. Then classify as

consistent & independent, consistent &

dependent, or inconsistent. a. 4x + 3y = 9 -2x +3y = -6

EXAMPLES3) Graph the linear systems. Then classify

as consistent & independent, consistent &

dependent, or inconsistent. b. -x + y = 3 y = x - 7