3. Review Systems of Equations: Elimination (3)
2x + 4y = 16
4x - 4y = -4
There are 3 methods to solving by elimination. The problem will
determine what method is used.
A) Solve by addition or subtraction. If the coefficients of one of the
variables are the same, that variable can easily be eliminated.
1) If the signs are different, add.
2) If the signs are the same, subtract.
(Or multiply one of the equations by – 1, then add.)
Solve the system of equations:
4. Review Systems of Equations: Elimination
-2x - 5y = -4
6x + 15y = 12
There are 3 methods to solving by elimination. The problem will
determine what method is used.
B) Solve by multiplying one of the
equations.
Solve the system of equations:
If the coefficient of one of the variables goes evenly into the other
coefficient, then multiply every term by the number which makes
the coefficients the same. Multiply by a negative number if the signs
are currently the same.
5. Review Systems of Equations: Elimination
5x - 2y = 7
-3x - 5y = 2
There are 3 methods to solving by elimination. The problem will
determine what method is used.
C) Solve by multiplying both of the equations.
Solve the system of equations:
If none of the coefficients are factors of the other, then select a
variable and find the LCM of the two coefficients. One of the
equations may have to be multiplied by a negative number to make
the signs different.
6. Review Systems of Equations: Substitution (2)
x = - 3y - 4
2x + 5y = - 6
With substitution, we are trying to rearrange an equation to say
y = .... or x = .... You have many options. Choose the easiest variable to
solve for. We then take out the x or y in the other equation, and
replace it with the right side of the equation we just solved for.
Solve the system of equations
by substitution:
We then have one equation with one variable to solve
for.
After solving for the first variable, plug it back into the 2nd equation,
and solve for the remaining variable.
2x - 4y = 12
x - 3y = 11
For this system, you must rearrange one of the
equations to solve for x or y
Which variable is the easiest to solve
for?
7. Applying Systems of Equations:
Prom tickets cost $10 for singles and $15 for couples.
Fifty more couples tickets were sold than were singles
tickets. Total ticket sales were $4000.
How many of each ticket type were sold?
8. Solving Systems of Inequalities (2)
Practice 1. Find the solution to:
x + y < 1; x - y > 1
1: Rewrite in slope-intercept form:
x - y > 1;
2: Graph the first line.
3: Lightly shade the correct side
of the line.
4: Repeat steps 2 & 3 for the 2nd
line.
5: Heavily shade the
overlapping areas, which is the
solution.
x + y < 1;
y < x - 1
y < -x + 1
10. The sum of three numbers is 14. The largest is 4 times the
smallest. The sum of the smallest and two times the largest is
18. Find the numbers. ( In the form (smallest, middle, largest
number)).
Solving a 3x3 System of Equations (1)
x + y + z = 14 z = 4xx + 2z = 18
How many solutions does the system have:
12x - 8y = 20
3x - 2y = 5
How many solutions does the system have:
Which point is a solution to
the following system?
2y – x > - 6
2y – 3x < - 6
A) (- 4, - 1) B) (3, 1) C) (0, - 3) D) (4, 3) E) None
x y z
Solve by SubstitutionOther Problems (3)
11. Changes to Class Work 3.4:
A) Do not do Systems of Inequalities #3
B) Make the
following changes:
