SYSTEM OF EQUATIONS
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?
Choices:
A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4
Correct Answer: B
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.
Quick Summary
- A system of equations consists of multiple equations.
- The solution to a system of equations is the set of values that satisfy all equations simultaneously.
- Graphically, the solution is the point of intersection of the equations.
🍎 Teacher Insights
Emphasize the graphical representation of systems of equations to aid understanding. Use real-world examples to illustrate the application of systems of equations.🎓 Prerequisites
- Solving linear equations
- Graphing linear equations
- Basic algebra
Check Your Knowledge
Q1: Which of the following is a solution to the system of equations: x + y = 5, x - y = 1?
Q2: How many solutions does the following system of equations have: y = 2x + 3, y = 2x + 5?
Frequently Asked Questions
Q: How do I know if a system of equations has no solution?
A: If the lines are parallel and do not intersect, the system has no solution.
Q: What does it mean for a system to have infinite solutions?
A: If the equations represent the same line, every point on the line is a solution, resulting in infinitely many solutions.