Download 3.1 System of Equations

7.1 System of Equations
Solve by graphing
• A system of linear equations consists of
two or more linear equations:
• For example:
5x + 6y = 14
2x + 5y = 3
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
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