## Definition Of System Of Equations

A system of equations is a set of two or more equations with the same variables, graphed in the same coordinate plane

### Examples of System of Equations

The figure below shows the graph of the system of equations
2x + 3y = 6 , x - y = 3

### Video Examples: System of Equations centered cubic fcc Thier point of intersection gives the solution of the system of equations.

### Solved Example on System of Equations

#### Ques: Which of the graphs represents the system of equations - 2x + 3y > 6 and x + y = - 3? A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

### Solution:

Step 1: Graph -2x + 3y > 6 on a coordinate plane. Step 2: Graph x + y ≤ -3 on the same coordinate plane. Step 3: The solutions are the coordinates of all the points in the region that is shaded in both colors.
Step 4: Check whether the solution (-4, 0) satisfies the two inequalities or not.
Step 5: -2x +3 3y > 6
-(-2) + 3 (0) > 6 [Replace x with -4 and y with 0.]
Step 6: 8 > 6 [ True]
Step 7: x + y ≤ -3
-4 + 0 ≤ - 3 [Replace x with -4 and y with 0.]
Step 8: -4 ≤ -3 [True.]
Step 9: Since the graph in step 2 matches with the graph 2 of choice B, Graph 2 represents the system of equations.