Transcript Solving a system of equations by SUBSTITUTION

Solving a system of equations by SUBSTITUTION
Step 1: Solve an equation for
one variable.
Pick the easier equation. The goal
is to get y= ; x= ; a= ; etc.
Step 2: Substitute
Put the equation solved in Step 1
into the other equation.
Step 3: Solve the equation.
Get the variable by itself.
Step 4: Plug back in to find the
other variable.
Substitute the value of the variable
into the equation.
Step 5: Check your solution.
Substitute your ordered pair into
BOTH equations.
1) Solve the system using substitution
x+y=5
y=3+x
Step 1: Solve an equation for
one variable.
The second equation is
already solved for y!
Step 2: Substitute
x+y=5
x + (3 + x) = 5
Step 3: Solve the equation.
2x + 3 = 5
2x = 2
x=1
1) Solve the system using substitution
x+y=5
y=3+x
Step 4: Plug back in to find the
other variable.
Step 5: Check your solution.
x+y=5
(1) + y = 5
y=4
(1, 4)
(1) + (4) = 5
(4) = 3 + (1)
The solution is (1, 4). What do you think the answer would
be if you graphed the two equations?
Solve the system using substitution
3x – y = 4
x = 4y - 17
Solving a system of equations by SUBSTITUTION
Step 1:
Step 2:
Step 3:
Step 4:
Pick the easier equation. The goal
is toisget
y= ;y=
x=; ;x=
a=; ;aetc.
to get
Using the equation solved in Step 1
. solved
the variable
in the
other1
Put replace
the equation
in Step
equation. Therefore you have one
into the other equation
equation with one variable.
he variable by itself.
Get
theeasier
variable
by itself.The goal
ck the
equation.
is to get y=.; x= ; a= ; etc
Substitute the value of the
variable into the equation.
Write your answer as an
ordered pair (x, y).
REAL WORLD APP
• You buy a total of 50 burgers and hotdogs for
$90. You pay $2 per burger and $1.50 per
hotdog.
Write a system of equations to find the number
of x burgers and y hotdogs.
Solve the system by substitution
_______burgers and ______hotdogs
Try this:
• You sell lemonade for $2 per cup and orange
juice for $3 per cup. You sell a total of 100
cups for $240.
Write a system of equations to find the number
of x cups of lemonade and y cups of orange
juice.
Solve the system by substitution
_______cups lemonade & ______cups orange juice