Download Section 3.1

Algebra 2CP
Day 16
3.1 Graphing Systems of Equations
o Daily Openers
o Check homework
3.1 Graphing Systems of Equations
linear system – two or more lines graphed on the same coordinate plane.
solution (of a system) – the point(s) where the graphs intersect.
– the ordered pair that makes all the equations TRUE.
Ex. Decide if the point is a solution to the equation.
3x + y = 4
(2, 1), (-3, 2)
-x + 3y = -5
Ex. Decide if the point is a solution to the equation.
x + y = -2
(-2, 3), (-3, 1)
2x – 3y = -9
Ex. Solve:
y = 2x – 3
y=x–1
Ex. Solve:
y = 2x – 6
y = -½x + 4
Ex. Solve:
4x – 3y = -6
4x – 2y = 0
Ex. Solve:
x – 8y = -40
-5x + 8y = 8
Ex. Solve:
x + y = -1
2x –y = -8
Ex. Solve:
4x + 5y = 20
/4x + y = 4
5
Ex. Solve:
2x – 3y = 8
4x + 3y = -2
Ex. Tony has $90 in his savings account and starts saving $5 a week. Lindsey has $40 in her
savings account and starts saving $15 a week. After how many weeks will they have the
same amount of money? What does the point of intersection mean?
Ex. A total of $25000 is invested in two funds paying 5% and 6% annual interest. The combined
annual interest is $1400. How much of the $25000 is invested in each fund?
NUMBER OF SOLUTIONS OF LINEAR SYSTEMS
INDEPENDENT
INCONSISTENT
DEPENDENT
Different Slopes
Parallel Lines
Same Slopes
(different y-int.)
Coincident Lines
Same Slopes
(same y-int.)
Ex. How many solutions does each system have?
(a)
(c)
(e)
 2x  4 y  1
x  2y  3
2x  y  4
 4 x  2 y  8
x y 2
 3x  3 y  6
(b)
(d)
(f)
3x  2 y  6
 6 x  4 y  12
 x  y 1
x  y 1
x  2y  6
x  2y  2
Homework – pages 120 – 121 #1–9 all, 11–24 all, 25–35 Odd
Daily Openers – 1. Graph the line: -x + y = 3
2. Graph the line on the same axis as #1: 4x + 5y = -3
3. At what point do the two lies intersect.
4. Graph the line y = 8
5. Graph the line x = -2