Unit 3 Lesson 2 Day 2 – Systems of Linear Equations
Name:________________________________
Date:___________________ Hr:__________
OBJECTIVE: I will be able to solve a system of linear equations by graphing, substitution, and elimination through use of
in-class notes and activities.
SOLVING SYSTEMS BY GRAPHING
When do we use this method: We solve by graphing when both equations can be easily graphed on a coordinate plane.
How do we use this method:
1.
Graph the two given lines
2.
Find the point of intersection.
To Graph:
It will always be one of these four forms – figure out which form first!
y = mx + b
Ax + By = C
x=a
1. Plot a point at the
1. Cover up the x-term
Vertical line
y-intercept (b)
and solve for y through the x-axis
2. Move to a second point
this is the y-intercept
at a
according to the slope =
2. Cover up the y-term
rise over run
and solve for x 3. Find as many other
this is the x-intercept
points as you can using
3. Plot the intercepts and
the slope
draw a line through them
4. Draw the line
1.
y=2
x = -3
2.
y = 2x + 1
y = - 4x – 5
3.
y=b
Horizontal line
through the y-axis
at b
2x + 4y = 12
x + 4y = 8
Unit 3 Lesson 2 Day 2 – Systems of Linear Equations
Name:________________________________
Date:___________________ Hr:__________
4.
y=7
y = -x + 4
5.
y = 5x + 11
y = -3x – 13
6.
y = 4x + 2
2x – y = -8
7.
2x + 4y = 8
3x + 7y = 13
8.
5x – 2y = -16
-3x + 2y = 12
9.
2x + 3y = 7
6x + 9y = 21
Name:________________________________
Date:___________________ Hr:__________
Unit 3 Lesson 2 Day 2 – Systems of Linear Equations
OBJECTIVE: I will be able to solve a system of linear equations by graphing, substitution, and elimination through use of
in-class notes and activities.
SOLVING SYSTEMS BY SUBSTITUTION
When do we use this method: When (1) you cannot graph and (2) at least one equation begins “y=” or “x=”
How to use:
1. Identify the variable that is isolated
(x = or y =) and circle what it equals.
Example:
y = 2x - 8
3x + 2y = 5
2. Plug the circled value into the other equation
for the isolated variable. (in parentheses)
3x + 2(2x – 8) = 5
3. Solve the equation for the remaining variable
3x + 4x – 16 = 5
7x
– 16 = 5
+ 16 +16
7x
= 21
7
7
x
=3
4. Plug the answer from step 3 into either equation
and solve for the other variable.
(note – if one variable was solved for
in step 1, you do not have to do this)
y = 2x - 8
y = 2(3) – 8
y=6 -8
y=2
5. Write your final answer as a point.
(3, 2)
4.
y=7
y = -x + 4
5.
y = 5x + 11
y = -3x – 13
6.
y = 4x + 2
2x – y = -8
Unit 3 Lesson 2 Day 2 – Systems of Linear Equations
1.
y=2
2.
y = 2x + 1
x = -3
y = - 4x – 5
7.
2x + 4y = 8
3x + 7y = 13
8.
5x – 2y = -16
-3x + 2y = 12
Name:________________________________
Date:___________________ Hr:__________
3.
2x + 4y = 12
x + 4y = 8
9.
2x + 3y = 7
6x + 9y = 21
Name:________________________________
Date:___________________ Hr:__________
Unit 3 Lesson 2 Day 2 – Systems of Linear Equations
OBJECTIVE: I will be able to solve a system of linear equations by graphing, substitution, and elimination through use of
in-class notes and activities.
SOLVING SYSTEMS BY ELIMINATION
When do we use this method: When (1) we can not use graphing and (2) both equations are written in standard form
(Ax + By = C).
How do we use this method:
These steps tell you how to eliminate x You can chose to eliminate y (just switch
all x's and y's in these directions)
Example:
2x + 5y = 16
3x + 2y = 2
1. Multiply the first equation by the
number in front of x in the second and vice-versa
except, SWITCH ONE OF THE SIGNS!
3(2x + 5y = 16)
-2(3x + 2y = 2)
6x + 15y = 48
-6x – 4y = -4
2. Add the resulting equations (only add like terms)
11y = 44
3. Solve the remaining equation for y by division
11y = 44
11
11
y = 4
4. Plug the solution from step 3 in one of the equations
for y
2x + 5(4) = 16
5. Solve the equation from step 4 for x.
2x + 20 = 16
- 20 - 20
2x
= -4
2
2
x
= -2
6. Write the solution as a point.
(-2, 4)
7.
2x + 4y = 8
3x + 7y = 13
8.
5x – 2y = -16
-3x + 2y = 12
9.
2x + 3y = 7
6x + 9y = 21
Unit 3 Lesson 2 Day 2 – Systems of Linear Equations
Name:________________________________
Date:___________________ Hr:__________
1.
y=2
x = -3
2.
y = 2x + 1
y = - 4x – 5
3.
2x + 4y = 12
x + 4y = 8
4.
y=7
y = -x + 4
5.
y = 5x + 11
y = -3x – 13
6.
y = 4x + 2
2x – y = -8