Download TOPIC # 8 – 6: Solving Systems by Elimination

Unit 6: Systems of
Equations
Algebra I
2011-2012
TOPIC # 8 – 3: GRAPHING SYSTEMS OF EQUATIONS
Solve each system by graphing.
Put each equation into y= mx + b form then use y= in your
calculator to graph the system.
1. y = 2x – 8
y = -x +1
m = _______ b = ______
m = _______ b = ______
Intersection __________
2. 2x + y = 2
x–y=4
y=
x+
m = _______ b = ______
y=
x+
m = _______ b = ______
Intersection __________
3. x – 3y = 6
x – 3y = -3
y=
x+
m = _______ b = ______
y=
x+
m = _______ b = ______
Intersection __________
4. 2x – y = 1
6x – 3y = 3
y=
x+
m = _______ b = ______
y=
x+
m = _______ b = ______
Intersection __________
State whether the given ordered pair is a solution to the system.
Show all work and circle yes or no.
1
5. y = 2 x + 2
Y=x–2
(8,6)
Yes or No
6. 2x – y = 1
-3x + y = 4
( 2, -1 )
Yes or No
7. 2x + 3y = 6
X – 4 = 2y
( 4, -1 )
8. y = 3x – 2
2x – y = 4
( -2, -8)
Yes or No
Yes or No
Solving Linear Systems by Graphs and Tables
(pp. 1 of 4)
A _________________________ is two (or more) equations comprised of two (or more) related
variables.
5x + 3y = 6
X – 4y = 9
The solution for the first equation above is a set of points represented by the line
y = -5/3x + 2
The solution for the second equation above is a set of points represented by the line
y = ¼ x – 9/4
The solution for the system of equations is the point or set of points where the two lines
intersect.
The intersection can occur in three different ways. The different possible solutions can be seen in
the alignment of the two lines when graphed on a plane.
(x,y)
R
Ø
Solving Linear Systems by Graphs and Tables
(pp. 2 of 4)
Systems of linear equations can be solved using
 ____________________________
 ____________________________
 ____________________________
o ____________________________
o ____________________________
Solve systems ______________________
A. Graph both equations by one of the following methods.
 Find the y-intercept (0, y) and x-intercept (x, 0), and draw the line through the intercept points.
 Solve each equation for y, and graph using slope (m) and y-intercept (b).
 Solve each equation for y, and enter them into the graphing calculator in y1 and y2. When
using the graphing calculator, the WINDOW may need to be adjusted so that the intersection
of the lines is viewable in the window.
B. Find the intersection point of the two lines.
 Read the point from the graph.
 Use the graphing calculator and graph the lines. Press 2nd CALC, select INTERSECT, get the
cursor close to the point of intersection, and ENTER ENTER ENTER.
 Verify the solution by checking the table function of the calculator. The solution will be the x
value where both values in y1 and y2 of the table are equal.
Example
y=x–4
y = -x + 10
X
Y1
X
Y2
Solving Linear Systems by Graphs and Tables
(pp. 3 of 4)
Guided Practice:
2. y = 3 – x
y=x+1
X
Special Cases:
3. y = 1/2x – 3/2
4y -2x = -6
Y1
4. 2y – x = 3
4y – 2x = -3
X
Y2
Solving Linear Systems by Graphs and Tables (pp. 4 of 4)
Practice Problems:
Find the solutions to the following systems of equations. Round solutions to the nearest tenth.
System
9.
x+y=4
2x + y = 6
10.
X – y = -5
X+y=3
11.
3x + y = -2
4x + y = -4
12.
X–y=0
5x – 3y = 10
13.
X + 2y = 1
5x – 4y = -23
14.
4x + 3y = 8
X – 2y = 13
15.
10x + 16y = 140
5x – 8y = 60
16.
2x + 3y = -12
8x – 5y = 40
Y = mx + b form
Sketch of graph
Solution
Check by table
TOPIC # 8 – 4: Solving Systems of Equations by
Substitution
1. y = 3x
x+y=8
Solve for a single
variable(get in y=)
Substitute and
Solve(plug n chug)
Find other value
and write solution
Intersection______
2. 2x + y = 9
x + 4y = 1
Solve for a single
variable(get in y=)
Substitute and
Solve(plug n chug)
Find other value
and write solution
Intersection______
3. 2a – b = 1
5a – 3b = 0
Solve for a single
variable(get in y=)
Substitute and
Solve(plug n chug)
Find other value
and write solution
Intersection______
4. 2x – y = 8
x+y=1
Solve for a single
variable(get in y=)
Substitute and
Solve(plug n chug)
Find other value
and write solution
Intersection______
TOPIC # 8 – 5: SOLVING SYSTEMS BY ELIMINATION
PART 1
Solve each system by ELIMINATION.
1. 5x – y = 12
3x + y = 4
2. 6c + 7d = -15
6c – 2d = 12
Solution:__________
Solution:__________
3. 8m + 12n = 20
5m + 12n = -1
4. 4x – 3y = -2
2x + 3y = 26
Solution:__________
Solution:__________
TOPIC # 8 – 6: Solving Systems by Elimination The Sequel
Solve each system by elimination.
1. 2x – 3y = 4
x + 4y = -9
Solution:__________
2. 4x – 5y = 23
3x + 10y = 31
Solution:__________
3. 4s – 5t = 3
3s + 2t = -15
Solution:__________
4. 3a + 4b = 2
5a + 9b = 1
Solution:__________