Unit 5 Section 2 Systems by Substitution.notebook
March 09, 2015
Solve a System of Equations by Substitution
Unit 5
Section 2
Unit 5 Section 2 Systems by Substitution.notebook
March 09, 2015
Systems of Equations
Solve a System of Equations by Substitution
To solve a system of equations by Substitution:
1) In either equation, solve for one variable in terms of
the other.
2) Substitute for that variable in the other equation.
Solve.
3) Substitute the result from Step 2 in either equation.
Solve for the other variable.
4) Check the solution in both original equations.
Unit 5 Section 2 Systems by Substitution.notebook
March 09, 2015
When does a problem lend itself to the substitution method?
When the coefficient of one of the variables of 1 or ­1.
Which two systems are set up for the substitution method? How could you tell?
Unit 5 Section 2 Systems by Substitution.notebook
March 09, 2015
Systems of Linear Equations by Subsitution still have three different types of solutions:
One Solution (Consistent and Independent) ­ variable equals one number
Example:
x = 3
y = 7
No Solution (Inconsistent) ­ variables cancel out, false statement
Example: 6 = 8
Infinitely Many Solutions (Consistent and Dependent) ­ variables cancel out, true statement
Example: 8 = 8
Unit 5 Section 2 Systems by Substitution.notebook
March 09, 2015
Solve the systems of equations using substitution. Write no solution or
infinitely many solutions where appropriate.
1.)
2.)
3.)
4.)
5.)
6.)
7.)
8.)
Unit 5 Section 2 Systems by Substitution.notebook
March 09, 2015
Keystone Ready
Nolan has $15.00, and he earns $6.00 an hour babysitting. The equation below can be used to determine how much money in dollars ﴾m﴿ Nolan has after any number of hours of babysitting ﴾h﴿.
m = 6h + 15
A. After how many hours of babysitting will Nolan have $51.00?
Claire has $9.00. She makes $8.00 an hour babysitting.
B. Use the system of linear equations below to find the number of hours of babysitting after which Nolan and Claire will have the same amount of money.
m = 6h + 15
m = 8h + 9