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