1. 7.1 System of Equations
Solve by graphing

2. A system of linear equations consists of two or more linear equations:
For example:
5x + 6y = 14
2x + 5y = 3

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 ? 3 Is ? 3
3 = 3 yes = 3 yes
Is 5·1-2 ? Is 5·(-4)-7 ? -27
5 - 2 ? – 7 ? -27
-3 = -27 no = -27 yes
So (1,2) is not the So (-4,7) is the solution
Solution of the system

4. 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)

5. 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

6. Solve by Graphing Ex 1) 3y – 2x = 6 -12y + 8x = -24
There are infinite numbers of solution because the lines are coinciding

7. A system of equations is consistent if they have at least one solution
A system of equation is inconsistent if they have no solution