[size=150]The equation of the blue line is fixed as 4x - 2y = 7[/size]
[size=150]Change the values of a, b and c so that the two lines have no intersections. [/size]
[size=150]How do you pick the values of a, b and c so that there are no intersections? [/size]
Look at the coefficient matrix. [br]Find the determinant of the coefficient matrix.
Now, use the same values of a and b as you used above. [br]Change the value of c so that the two lines are coincident. [br][br]What is the determinant of the coefficient matrix?
What can we tell about the number of intersections if the determinant of the coefficient matrix is 0?
Maybe no solutions or infinitely many solutions.
What can we tell about the determinant if there is exactly one intersection?
Determinant is not equal to 0.
Why is it related to determinants? [br][br]Feel free to share your idea.
Two equations are given in a 3D plot. [br][br][math]x+2y+3z=5[/math][br][math]2x+3y+z=3[/math][br][br]Can you change the values of a, b, c and d so that [br][br]i) there is one intersection? [br]ii) there are no intersections? [br]iii) there are infinitely many intersections? [br][br]Investigate in the relationship between the number of intersections and the determinant of the coefficient matrix.