Name
Date
Period
Reflection #67 (4B)
In these sections I learned
1__how to solve systems of equations using substitution and elimination
To do that I solve for one variable then “plug” that variable into one of
the original equations. _
2)_how the slopes of parallel and perpendicular lines are different and
and that parallel lines never intersect because they rise and run at the
same rate. ___
1) Write the type of graph and how many solutions you will find for the given slope/yintercepts.
_intersecting___lines means different slope, same or different y-intercept and __one__ solution(s).
__parallel______lines means the same slope and different y-intercept and __no_______ solution(s).
___collinear____lines means the same slope and same y-intercept and _infinitely many_solutions(s).
2a) Given the following
equation tell whether to
solve using graphing,
substitution or elimination
and tell why.
y = -4x - 9
-2x – y = 3
___Solve this using
substitution because one of
the equations is solved for y
already_
2b) Given the following
equation tell whether to
solve using graphing,
substitution or elimination
and tell why.
y  2x  9
y  x  6
2c) Given the following
equation tell whether to
solve using graphing,
substitution or elimination
and tell why.
5x + 4y = -3
-4x – 6y = 2
_Solve by elimination b/c
both equations are in st.
form and I can find like but
opposite variables.
__Solve by graphing because
both equations are already
solved for y making them
easy to graph._________
3a) Find the solution of the system. Graph
3b) Find the solution of the system. Graph
the lines and label the intersection point, if
the lines and the label the intersection point,
any. and tell what type of system is
if any, and tell what type of system is
represented.
Slope-Intercept Form represented.
Slope-Intercept Form
𝟏
already in S-I
𝒚 = 𝟑𝒙 −𝟒
𝟐
𝟑
𝟐𝒙 + 𝟑𝒚 = −𝟑
𝒚= 𝒙−𝟏
𝟐
𝒚 = 𝟓𝒙 +𝟓
𝟐
𝟓
𝒚 + 𝟐 = (𝒙 + 𝟓)
Already in S-I
𝒚=
𝟐
𝒙
𝟓
System
System
Type?
Type?
Parallel
Intersecting
Number of
(3, -3)
Number of
Solutions?
one
Solutions?
none
3c) Find the solution of the system. Graph the
lines and the label intersection point, if any. and
tell what type of system is represented.
Slope-Intercept Form
3d) Find the solution of the system. Graph the
lines and the label intersection point, if any. and
tell what type of system is represented.
Slope-Intercept Form
𝑦 = 2𝑥 − 3
4𝑥 − 2𝑦 = 6
4𝑥 + 𝑦 = 3
𝑦 = −4𝑥 + 3
𝑥−𝑦=2
𝑦 =𝑥−2
𝑦 = 2𝑥 − 3
Lines
intersect
at every
System
System
Type?
Type?
Collinear
intersecting
Number of
point
(1, -1)
Solutions?
Number of
Infinitely
Solutions?
many
one
Given two lines, without graphing, determine if the lines are perpendicular.
4a)
−2𝑥 + 6𝑦 = 12
𝑚=
𝑦=
1
3
1
−3𝑥
4d) Write an equation in slope-intercept form that
is perpendicular to the line 𝑦 − 4 = 2(𝑥 + 3) and
contains the point (2, −6)
+2
1
𝑚 = −3
Perpendicular Lines? no
4b)
5𝑥 + 4𝑦 = 4
8𝑥 − 10𝑦 = 20
5
4
𝑚 = −4
𝑚 = −5
Perpendicular Lines? no
4c)
3
𝑦 = −2𝑥 −6
Perpendicular Line Equation
−2𝑥 + 3𝑦 = 12
3
𝑚 = −2
Perpendicular Lines? yes
2
𝑚=3
𝑦=−
1
−5
2𝑥
5a) Solve using substitution.
𝑦 =𝑥+1
−𝑥 − 3𝑦 = −11
5b) Solve using substitution.
5c) Solve using substitution.
𝑦 = 4𝑥 + 1
−4𝑥 + 2𝑦 = −2
𝑥 = −6𝑦 + 30
−2𝑥 + 𝑦 = −8
Solution ( -1, -3 )
Solution ( 2 , 3 )
5d) Solve using elimination.
Solution ( 6, 4 )
5e) Solve using elimination.
5f) Solve using elimination.
2𝑥 − 15𝑦 = 25
𝑥 + 5𝑦 = −25
3𝑥 − 4𝑦 = −14
−4𝑥 + 9𝑦 = 4
9𝑥 − 5𝑦 = −22
−2𝑥 + 2𝑦 = 4
Solution (-10 , -3 )
Solution (-10 , -4 )
Solution (-3 , -2 )
6) Jimmy solved s system of equations and arrived at an answer (-2,-5), in your own words
tell what the answer means with regards to a system of equations.
(-2, -5) is the the solution of this system of equations. One the graph of this
______________________________________________________________
system it would be the point of intersection of the two lines.
______________________________________________________________
______________________________________________________________
7) Given one equation of a system below write a second equation so that the system has:
Given Equation
One Solution
No Solution
2
𝑦 = 𝑥−5
3
𝑦 = 6𝑥 + 7
5
𝑦=− 𝑥
3
8) Follow the steps to create a system of equations that intersect.
1) Select a point for your solution and
label it. Solution (
)
2) Selcet a y-intercept for equation 1
y-intercept (b) ( 0,
)
3) Draw line for equation 1 through
the solution and the y-intercept, then
find the slope (m) =
.
4) Write the equation for line 1 in
slope-intercept form y =
.
5) Selcet a different y-intercept
for equation 2; y-intercept (b) ( 0,
)
6) Draw line for equation 2 through
the solution and this y-intercept, then
find the slope (m) =
.
7) Write the equation for line 2 in
slope-intercept form y =
.
Infinitely Many
Solutions