Download 2y = 2xана14 6x + 3y =ан3

Unit 8 Review
Name: _____________
Linear Systems
Hour: ____
Parallel & Perpendicular Lines
I can determine the number of solutions between a system of LT 1­3: linear equations. I can solve a system of linear equations by table, graph, and equation.
For 1­2, determine if the ordered pair is a solution to the system.
1) 2) {
2y ­ 8 = x 10y + 2x = 8
{
4y ­ 2x = 12
y ­ 6 = 3x
(­1.2, 2.4)
(6, 4)
3) {
Solve the Linear System using...
2y = 2x ­ 14
6x + 3y = ­3
(solution)
( , )
A) {
y = mx + b work
C) Graph
B) Table
x y
x
y
D) Equation
y
x
4) Which linear system has the solution (­3, 9)? 5) 6) Sketch a system of equations that has one solution.
7) Sketch a system of equations that has no solutions.
8) Sketch a system of equations that has infinite solutions.
9) Identify the number of solutions for 10) Identify the number of solutions for the system. Explain how you know.
the system. Explain how you know.
{
y + 3 = 2x
2y ­ 6 = 4x
{
{
{2y = x + 6
2x ­ 4y = ­12 11) Identify the number of solutions for 12) the system. Explain how you know.
{
{4x + 3y = ­15
y ­ 2 = x
I can write equations in slope­intercept form of parallel and LT 4­5: perpendicular lines.
1
13) A line has the equation y = x ­ 2. 7
Write an equation of a line that is parallel to this line?
14) A line has the equation y = 4x ­ 1. Write an equation that is perpendicular to this line?
15)What is the equation of the line that 16)
passes through (­10, 2) and is parallel to the line y = ­2x ­ 3
What is the equation of the line that passes through (­8, ­15) and is perpendicular to the line y = ­4x + 6.
y
y
x
x
m =
b =
(x, y) =
m =
b =
(x, y) =
17) A line has the equation y = ­8x ­ 5. What is the slope of a line perpendicular to this line? 18) A line has the equation x + 3y = 7. What is the slope of a line parallel to this line?
A. ­8
A. ­3
B. ­ 18
B. ­ 13
C. 1
8
C. 1
D. 8
D. 3
2
19) Determine if the lines are parallel, perpendicular, or none.
Line B
x + 3y = 10
Line A
m= 3x ­ y = 10
m= • Lines A and B are _________________________________________.
20) A line passes through (6, 4) and 21) A line passes through (8, ­5) and (5, ­5). Write an equation of a line that is parallel to it and passes through (­1, ­3).
(4, ­2). Write an equation of a line that is perpendicular to it and passes through (6, ­4).
4
A. y = x ­ 12
3
4
B. y = ­ x + 1
3
3
C. y = x ­ 8.5
4
4
D. y = ­ x + 4
3
22) What is the equation of the 23) What is the equation of the line that passes through (2, 4) and is parallel to x = ­3. line that passes through (2, 4) and is perpendicular to x = ­3. (Hint: graph the lines.)
y
(Hint: graph the lines.)
y
x
x
24)
25)
What is the correct name for a quadrilateral with slopes of 1, 5, 1, ­5.
26) One side of a rectangle has an equation y = ­3x ­ 1. What are possible equations for the other three sides?
A. rectangle
Side 1: y = ­3x ­ 1
B. rhombus
Side 2:
C. parallelogram
Side 3:
D. trapezoid
Side 4:
­3
2
Answers:
1) not a solution
2) solution
3) (2, ­5)
4) D
9) no solutions
13) sample answer
1
y = x + 3
7
10) infinite solutions
11) one solution
12) C
14) sample answer
1
y = ­ x + 6 4
15) y = ­2x ­ 18
5) D
1
16) y = x ­ 13 8)
7) 6) 17) C
4
18) D
19) perpendicular 20) y = 9x + 6 21) A 22) x = 2
23) y = 4
24) A
25) D
26) sample answer:
side 2: y = ­3x + 10
1
side 3: y = x + 5
3
1
3
side 4: y = x ­ 8