Solving a system of equations
by substitution WARM UP
SOLVE THE SYSTEM OF EQUATIONS
Y = -2X + 7
Y = X + 1
Y = -2X + 7
1 = Y – X
systems
 What kind of solutions do systems of
equations have?
 What kind of solutions do parallel lines have?
 What kind of solutions do the same line
have?
Solve using graphing
y = x + 3
y = -x + 7
Solve using graphing
 2y + 2x = 6
 3y - 3x = 3
Method for substitution
1. Choose one equation and solve for
x or y.
2. Substitute the expression from that
equation into the other equation
and solve.
3. Substitute the value found in step 2
back into the equation solved in
step one.
Solve using substitution
 4x – 2y = -6
 X + 3y = 9
Solve using substitution
 2x + y = 0
 5x – 4y = 26
Solving systems by elimination
1. Add the equations, eliminating one variable.
Then solve the equation.
2. Substitute to solve for the other variable.
 -6x – 4y = -10
 6x + 2y = 8
Solve the system using elimination
-x - 2y = 0
-6x + 2y = 14
Solve the system using elimination
 3X – 3y = 9
 -4x + 3y = 12
Solve the system using elimination
X – 5y = 2
3x + 5y = 6
Solve the system using elimination
X – y = 7
6x + y = 7
Solving systems by elimination
 What happens if the equations aren’t written
in a way that something can easily be added to
zero?
 NEW STEPS!
1. Choose which variable to eliminate x or y
2. Decide what to multiply by so that when you
add the desired variable eliminates.
3. Add the two equations together
4. Solve for the remaining variable
5. Substitute back in to one of the original
equations to solve for other variable.
What would you do to solve a system like this?
 3x + 2y = -6
 2x + 5y = 7
Solve using elimination
6x + 2y = 2
-3x + 3y = -9
Solve using elimination
2x - 3y = 4
-4x + 5y = -8
Solve using elimination
-2x = 2y - 4
-7x + 6y = 25
Solve using elimination
3x + 2y = 8
2y = 12 – 5x
Solve using elimination
-16x + 3y = -19
-8x – y = -7
Solve using elimination
-3x – 8y = 24
-4x – 5y = -2
Which Method To Use?

For each of the
systems of equations
shown, choose which
method would be the
best option to use in
solving the system:
A.
B.
C.
Substitution Method
Elimination Method
Graphical Method
  y  4x  2

 y  2 x  3
x  y  4
 
 x  y  12
 x  y  19

 4 x  16 y  34
Break even points
 A car company spends $8,900 to make each new car.
The company charges $12,900 for each new car. The
company also spent $60,000,000 on building the
new car plant. How many cars need to be sold to pay
for the new plant?
Word problem strategies
 Define variables - what in the problem don’t you
know?
 Define what you are looking for – what is the
problem asking you to find?
 Define equations – what information in the problem
can go together in an equation?
 Tyler is catering a banquet for 250 people. Each
person will be served either a chicken dish that costs
$5 each or a beef dish that costs $7 each. Tyler spent
$1500. How many dishes of each type did Tyler
serve?
more word problems
 The perimeter of a rectangle is 66 cm and its width is
half its length. What are the length and width of the
rectangle?
Which job?
 There are two different jobs Jordan is considering.
The first job will pay $4200 per month plus an
annual bonus of $4500. The second job pays $4100
per month plus $600 per month toward her rent and
an annual bonus of $500. Which job should she
take?
Word problem
 Two numbers added together is 7
 The difference of the two numbers is 1