Solving Systems of Solving Systems of Equations Using Equations Using

SubstitutionSubstitution

Solving Systems of Solving Systems of Equations Using Equations Using

SubstitutionSubstitution

Students will solve systems of Students will solve systems of equations using substitution.equations using substitution.

FHS Systems of Equations 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 1Use substitution to solve the system of

equations. 1

7

y x

x y

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.)

Step 3: Substitute the x-value into one of the original equations to solve for y.

x + y = 7

x + (x – 1) = 7

2x – 1 = 7

x = 4

Substitute (x –1) for y in the other equation.Combine like terms.

y = x – 1

y = (4) – 1

y = 3

Substitute x = 4.

The solution is the ordered pair (4, 3).

FHS Systems of Equations 5

Example 2Use substitution to solve the system of

equations.2 1

3 2 26

x

x y

y

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.)

Step 3: Substitute the x-value into one of the original equations to solve for y.

3x + 2y = 26

3x + 2(2x – 1) = 26 7x – 2 = 26

x = 4

Substitute (x –1) for y in the other equation.Combine like terms.

y = 2x – 1

y = 2(4) – 1

y = 7

Substitute x = 4.

The solution is the ordered pair (4, 7).