Transcript Systems of Equations - Pascack Valley Regional High School

Systems of Equations
Intermediate Algebra
Final Exam Review
1a. Solve by graphing
ì y = 2x + 3
í
î y = -3x + 8
(1,5)
1b. Solve by graphing
ì-12x + 4y = 8
í
î-3x + y = 4
ì 4y = 12x + 8
í
î y = 3x + 4
ì y = 3x + 2
í
î y = 3x + 4
Parallel lines
No solution
2a. Coincide, Intersect, Parallel?
ì5x - 7y = -7
ï
í
5
ï y = x +1
î
7
ì-7y = -5x - 7 isolate the y term
ï
í
5
ï y = x +1
î
7
ì
5
ïï y = x +1 simplify
7
í
ï y = 5 x +1
ïî
7
Lines coincide
2b. Coincide, Intersect, Parallel?
ì2x - 4y = 4
ì-4y = -2x + 4
í
í
î-x + 2y - 2 = 0 î2y = x + 2
ì
1
ïï y = x -1
2
í
ï y = 1 x +1
ïî
2
Parallel lines
isolate the y term
simplify
3a. Solve (substitution)
ì2x + 5y = 12
í
î x - 6y = -11
ì2x + 5y = 12
í
î x = 6y -11 isolate the x term
2(6y -11) + 5y = 12
2x + 5(2) = 12
12y - 22 + 5y = 12
17y = 34
2x +10 = 12
2x = 2
y =2
x =1
(1,2)
3b. Solve (elimination)
ì x - 2y = 9
í
î 4x + 3y = 14
11y = -22
y = -2
ì-4x + 8y = -36
í
î4x + 3y = 14
multiply
x - 2(-2) = 9
x+4=9
x =5
(5,-2)
4. Word Problem
Let x = # of Snickers
Let y = # of Milky Ways
ì x + y = 25
í
î x + 2y = 40
-y = -15
ì x + y = 25
í
î-x - 2y = -40
x +15 = 25
y = 15
x = 10
10 Snickers
15 Milky Ways
5. Graph the system
ì6x - 2y > 2
í
îx + y ³ 3
ì-2y > -6x + 2
í
î y ³ -x + 3
ì y < 3x -1
í
î y ³ -x + 3