

What does it mean?
How can you use elimination in the problem
below?
THINK BOX
Solve the system using
Elimination:
x + 2y = 7
3x – 2y = 5
Now try working on it with a partner
I can solve a system of equations using the
elimination method.
Same as before:

Find the point that is on both lines
◦ Where the lines intersect

Find the value for x and y
Step 1:
look for variables that are same value but opposite of each other
-5x + y = 0
5x + y = 10
The x’s have the same value and are
opposites!
Step 2:

ADD the equations to eliminate ONE of the variables and solve
for the remaining variable.
-5x + y = 0
-5x and 5x can be eliminated
+ 5x + y = 10
because they cancel each other
2y = 10
out! I can now solve for y.
2
2
y=5
Step 3: Solve for other variable by plugging in the known
variable value into either equation
y=5
ANSWER:
-5x + y = 0
5x + y = 10
x=1
y=5
Plug in 5 for y
5x + 5 =10
-5
-5
5x = 5
5
5
x=1
Point of
Intersection is
(1, 5)
The only step that changes is STEP 1.
 look for the variable that can be eliminated if…
x – 2y = -9
x + 3y = 16

The x’s could be eliminated if one of them were a negative.
Create the Cancellation
x – 2y = -9
-1(x + 3y = 16)
-x -3y = -16
• multiply either equation by -1
(remember to multiply through the entire
equation; both sides of the equal sign)
Step 2: same as before
 ADD the equations to eliminate ONE of the variables and
solve for the remaining variable.
x – 2y = -9
-x -3y = -16
-5y = -25
-5
-5
y=5
Step 3: Solve for other variable by plugging in the known
variable value into either equation
ANSWER:
x – 2y = -9
x – 2(5) = -9
x =1
x -10 = -9
-x -3y = -16
+10 +10
x=1
y=5
Point of
Intersection:
(1,5)
The only step that changes is STEP 1.
 look for the variable that can be eliminated if…
5x + 2y = 16
3x – 4y = 20

The y’s are opposite each other and can be eliminated IF the 2y
was a 4y!
Create the Cancellation
5x + 2y = 16
2 (5x + 2y = 16)
10x + 4y = 32
3x – 4y = 20
• multiply the first equation by 2
(remember to multiply through the entire
equation; both sides of the equal sign)
Step 2: same as before
 ADD the equations to eliminate ONE of the variables and
solve for the remaining variable.
10x + 4y = 32
3x – 4y = 20
13x = 52
13
13
x=4
Step 3: Solve for other variable by plugging in the known
variable value into either equation
10x + 4y = 32
3(4) – 4y = 20
ANSWER:
12 – 4y = 20
x =4
3x – 4y = 20
-12
-12
-4x = 8
-4
-4
x = -2
y = -2
Point of
Intersection:
(4, -2)
2x + 3y = 11
-2x + 5y = 13
6x + 5y = 19
2x + 3y = 5
4x + 5y = 35
2y = 3x - 9
On a Post It:
1.
2.
Write Name & Period
Where are you confused?