Download Lesson 3.1

3.1 System of Equations
Solve by graphing
Ex 1) x + y = 3
5x – y = -27
Which one is the solution of this system? (1,2) or (-4,7)
*Check (1,2)
Check (-4,7)
Is 1 + 2 ? 3
Is -4 + 7 ? 3
3 = 3 yes
3 = 3 yes
Is 5·1-2 ? -27
Is 5·(-4)-7 ? -27
5 - 2 ? -27
-20 – 7 ? -27
-3 = -27 no
-27 = -27 yes
So (1,2) is not the
So (-4,7) is the solution
Solution
of the system
Solve by Graphing
Ex 1) y – x = 1
y+x=3
y=x+1
y = -x + 3
Therefore the solution
of this system is (1,2)
(1,2)
Solve by Graphing
Ex 1) y = -3x + 5
y = -3x - 2
The lines are parallel,
so there is no solution
for this system of
equations
Solve by Graphing
Ex 1) 3y – 2x = 6
-12y + 8x = -24
3y = 2x + 6
-12y = -8x - 24
y = 2/3 x + 2
y = 2/3 x + 2
There are infinite
numbers of solution
because the lines are
coinciding
• A system of equations is consistent if they
have at least one solution
• A system of equation is inconsistent if they
have no solution
***When an equation in a system can be obtained by
multiplying both sides of another equation by a
constant, the two equations are said to be dependent
• A system of equations is dependent if it
has many solutions
• A system of equations is independent if it
has one solution or no solutions
Example
Y = -2
X=2
What is the solution? Dependent or
independent? Consistent or Inconsistent?
Answer: (2, -2), consistent, independent
Example
6x – 2y = 2
9x – 3y = 1
What is the solution? Dependent or
independent? Consistent or Inconsistent?
Answer: No solution; inconsistent,
independent
Example
Y=3-x
2x +2y = 6
What is the solution? Dependent or
independent? Consistent or Inconsistent?
Answer: Infinite many solutions; consistent,
dependent
Example
Y=4-x
Y=x-4
What is the solution? Dependent or
independent? Consistent or Inconsistent?
Answer: (4,0) consistent, independent