Transcript 3.1 Solving Systems of Equations by graphing.

3.2 Solving Systems of Equations
by algebraically.
Main Ideas
• Solve systems of linear equation by using
substitution.
• Solve systems of linear equations by using
elimination.
Systems of Equations
Three types of solutions
 One solution
The equations intersect in one point.

Infinitely many solutions
The equations are the same line.

No solutions
The equation do not intersect, parallel.
Substitution Method
One equation is solved for one variable. Then,
this expression is substituted for that
variable in the other equation.
Hint: It is easier to solve for a variable that has a
coefficient of 1.
If the variable cancels. Then there are two
possible answers
◦ Infinitely many solutions if the numbers are
equal.
◦ No solution if the numbers are not equal.
Solve using substitution.
1) 2x – 3y = 2
x + 2y = 15
2) x + 4y = 26
x – 5y = -10
Solve using substitution.
3) x + y = 1.5
3x + 3y = 4.5
4) y = 3x – 4
y=4+x
Elimination Method
Using this method, you eliminate one of the
variables by adding or subtracting the equations.
To eliminate a variable you must have
Same coefficients – add equations
Opposite coefficients– subtract equations
Sometimes you have to multiply an equation(s) to
get the coefficients you need to use elimination.
If the variable cancels. Then there are two possible
answers
◦ Infinitely many solutions if the numbers are equal.
◦ No solution if the numbers are not equal.
Solve using elimination method.
1) 2x + y = 4
2) 5b = 20 + 2a
3x + y = 8
2a + 4b = 7
Solve by using elimination.
5) 2x + 3y = 12
6) x + y = 3
5x – 2y = 11
2x + 2y = 6
Real World problems
Keys to solving two variable equations.
1. Read carefully and be organized.
3. Write two equations.
4. Solve the system of equations.
5. Answer the question and label.
Campus Rentals rents 2 and 3 bedroom apartments
for $700 and $900 per month, respectively. Last
month they had six vacant apartments and
reported $4600 in lost rent. How many 2 bedroom
apartments were vacant?
Lancaster Woodworkers Furniture Store builds two
types of wooden outdoor chairs. A rocking chair
sells for $265 and an Adirondack chair with
footstool sells for $320. The books show that last
month, the business earned $13,930 for the 48
outdoor chairs sold. How many rocking chairs were
sold?