Transcript SYSTEMS OF EQUATIONS

SYSTEMS OF EQUATIONS
Substitution Method
Ex. 1:
2x + y = 15
y = 3x
You
have
to
go
back
to
Wenow
have
been
using
the
2x + 3x
= 3(3)
15 = 9
y
=
one of your
original in
equations
Substitution
Property
our proofs.
where
you
will
substitute
the
so
5x
=
15
Nowanswer
we are going
toordered
Write your
as
an
known value of x in
use substitution
to
solve
pair
order toand
determine
x = (3,
3 the9)value of y
systems of equations.
Ex. 2
3x – y = 13
y=x+5
3x – ( x + 5 ) = 13
3x – x – 5 = 13
Now substitute back into one of
2x = 18 to find y.
the original equations
y = 9 + 5 = x14
=9
You may have to rearrange one of
the equations before you do the
substitution.
x + 4y = 20
Rearrange:
x = 20 – 4y
2x + 3y = 10
Now substitute and solve for y:
Find x: x + 4(6) = 20
2 (20 – 4y)+3y=10
so=4020– 8y + 3y=10
x+ 24
-5y = -30 so y =x 6= -4
Solving systems of equations by
adding or subtracting equations
Example: x + 5y = -7
3x – 5y = 15
Now substitute into either equation
youy:add these
toIffind
4x = 8 two equations
2 + 5y =the
-7 5y
= -9 drops out!
together,
y term
x=
2
y = -9/5
Example:
4x – y = 16
3x – y = 11
x=5
4(5) – y = 16
20 – y = 16
y=4
(5, 4)
You may have to multiply one of the
equations before you add or
subtract:
-3x + 2y = 10
Now add
the
equations
together
4x
-4
2x––2y
y == -2
Multiply this
equation
by 2
x=6
After substitution we find
y = 14
(6,14)
You may have to multiply both of
the equations by a number to get a
variable to cancel out.
Multiply by 3 6x
2x++15y
5y == 108
36
3x-–4y2y= =
6x
-6-3
19y = 114
y= 6
Multiply by 2