Algebra II
Notes – 3.1 Solving Linear Systems By Graphing
System of Two Linear Equations – Equations of two lines in the form Ax + By = C and Dx + Ey = F.
Solution – a point (x, y) that satisfies both equations in the system.
Two Lines in a Plane Can Do One of Three Things:
1.) Intersect at exactly one point.
2.) Do not intersect (parallel lines).
3.) The two lines coincide (are the same line).
(one solution)
(no solution)
(infinite number of solutions.)
EX: Solve the system by graphing: (First solve both equations for y, then graph both lines. Determine
the point where the lines cross.)
⎧ x − y = −4
⎨
⎩x + y = 2
4
2
-5
5
-2
-4
What is the downside of solving by graphing?
EX: Solve each by graphing:
4
⎧2 x + y = 13
a.) ⎨
⎩5 x − 2 y = 1
2
-5
5
-2
-4
⎧2 x + 4 y = 12
b.) ⎨
⎩x + 2 y = 6
4
2
-5
5
-2
-4
c.)
⎧x − y = 5
⎨
⎩2 x − 2 y = 9
4
2
-5
5
-2
-4
Day 1: Assign p. 142 #11 – 31 Odd
Day 2: Assign p. 142 #32 – 34, 41, 42, 44, 46, 47, 51, 54