1. Solving Systems of Equations Using Substitution
Connections - Tuesday, November 9
Unit D.3
Solving Systems of Equations Using Substitution
Students will solve systems of equations using substitution.
Unit D.3 - Soving Systems Using Substitution

2. Why Not Use Graphing?
This graph shows a system of linear equations. As you can see, determining the solution from the graph is not easy.
But, you can use the substitution method to find an exact solution.
In substitution, you solve one equation for one
variable and then substitute this
expression into the other equation.
FHS
Systems of Equations

3. Using Substitution – Example 1
Use substitution to solve the system of equations.
Step 1: Solve one equation for one variable. The first equation is already solved for y :
y = x – 1
Step 2: Substitute the expression into the
other equation.
FHS
Systems of Equations

4. Example 1 (cont.) x + y = 7 x + (x – 1) = 7 2x – 1 = 7 x = 4
Substitute (x –1) for y in the other
equation.
x + (x – 1) = 7
2x – 1 = 7
Combine like terms.
x = 4
Step 3: Substitute the x-value into one of the original equations to solve for y.
y = x – 1
y = (4) – 1
Substitute x = 4.
y = 3
The solution is the ordered pair (4, 3).
FHS
Systems of Equations

5. Example 2 Use substitution to solve the system of equations.
Step 1: Solve one equation for one variable. The first equation is already solved for y :
y = 2x – 1
Step 2: Substitute the expression into the
other equation.
FHS
Systems of Equations

6. Example 2 (cont.) 3x + 2y = 26 3x + 2(2x – 1) = 26 7x – 2 = 26 x = 4
Substitute (x –1) for y in the other equation.
3x + 2(2x – 1) = 26
7x – 2 = 26
Combine like terms.
x = 4
Step 3: Substitute the x-value into one of the original equations to solve for y.
y = 2x – 1
y = 2(4) – 1
Substitute x = 4.
y = 7
The solution is the ordered pair (4, 7).
FHS
Systems of Equations