Hi everyone,

I just need help with this assignment question. If anyone can solve it, you can have fg however much you want since I rarely go on here.

1. Consider the system below. Identify how many solutions this system will have (without actually solving for x and y).
Hint: Calculate determinant of the co-efficient matrix.

4x + 3y = -4
y = 2x -3

Put your equations into a standard form :
4x + 3y = -4
-2x + 1y = -3

Consider the matrix formed with the coefficients of x and y :

( 4 3 )
(-2 1)

Compute the determinant of that matrix :

4*1 - 3*(-2) = 4 + 6 = 10

If det ≠ 0, then your system has exactly 1 solution (x;y).
If det = 0, then your system may show 0 solution, or an infinite number of solutions.