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
EXAMPLES
2) Graph the linear system and estimate the
solution. Then check the solution algebraically.
a. y = –3x + 5
y = 2x – 5
EXAMPLES
2) Graph the linear system and estimate the
solution. Then check the solution algebraically.
b. 3x + y = 7
y = 2x - 3
EXAMPLES
3) Graph the linear systems. Then classify as
consistent & independent, consistent &
dependent, or inconsistent.
a. 4x + 3y = 9
-2x +3y = -6
EXAMPLES
3)
Graph the linear systems. Then classify as
consistent & independent, consistent &
dependent, or inconsistent.
b. -x + y = 3
y=x-7