World 3-8
Addition Method to Solve a System
Recall that a _______
system of two linear equations can
be solved by using let y1=y2 ie the ________________.
comparison method
Consider the following system of equations.
6x + 4y = 14
-6x +9y = 12
Instead of re-arranging to isolate y, simply add them up.
6x + 4y = 14
-6x + 9y = 12
13y = 26
13
13
y=2
sub y =2 to find x
6x + 4(2) = 14
-8
-8
6x = 6
x =1
(1, 2) is the solution
-6x + 9(2) = 12
-18 -18
-6x = -6
x =1
He offered her gifts and
what happened??
He left
thetohouse
because
he was
And
went
the beach
to cheer
up
heartbroken …..
In some cases the system will need to be adjusted
before a variable can be eliminated.
Eg. 1
3x + 4y = 19 x 2 Step 1 Multiply both equations so
2x - 5y = -18 x -3 that one variable can be eliminated
6x + 8y = 38
-6x +15y = 54
23y = 92
23
23
y=4
3x + 4(4) = 19
3x = 3
x =1
Step 2 Add the equations together to
solve the unknown
Step 3 Check answer by re-substituting the
variable Into both equations
2x -5(4) = -18
2x = 2
x =1
(1, 4) is the solution
So he
to get some
exercise
Hedecided
wasn’t cheered
up yet….
Eg. 2 Solve
x - 2y = -9
x + 3y = 16 x -1
x + -2y = -9
-x - 3y = -16
-5y = -25
-5 -5
y=5
Check sub y =5 to find x
x – 2y = -9
x – 2(5) = -9
x – 10 = -9
x=1
x + 3y = 16
x + 3(5) = 16
x =1
(5, 1) is the solution
Eg. 3 Confidence Builder
x - 2y = -9
x + 3y = 16 x -1
x + -2y = -9
-x - 3y = -16
-5y = -25
-5 -5
y=5
Check sub y =5 to find x
x – 2y = -9
x – 2(5) = -9
x – 10 = -9
x=1
x + 3y = 16
x + 3(5) = 16
x =1
(5, 1) is the solution
Ummm……..
I have to go Will
fix my
hair
you be my Valentine?
Team Challenge
Addition Method
1. Solve the System
2x + y = -4
x -y=4
2. Solve the System
3x + 4y = 24
x +y=7
3. Solve the System
2x + 8y = 8
-2x + y = 10
4. Solve the System
x - 2y = 10
3x - y = 0
5. Solve the System
3x -4y = -15
5x -y = -15
After
doing
all
of these
things,
he finally
In trying
impress
Ms.
Relation,
he
Plustohe
realized
they
should
How
to
For
solve
now.
a
linear
system!
realized
something…..
learnt
new
justsomething
be friends…….
Mini- Quiz
1. Find the POI between
7x - y = 20
and
y=x2 + x -12
2. Find the POI between
3x + y +6 = 0
and y=2x2 - 7x + 4
3. Find the POI between
y=x2 – 1 and x + y + 2 = 0