Question

4 equations and 3 unknowns ,is unique solution exixt

Answer 1

My approach to this would be to put the first three equations in echelon form by starting a Gaussian Reduction. For example :

x+3yy++2zz3z===13610

Then, I would express the left side of the fourth equation in terms of the first three ones. It's easy since the three equations are in triangular form. Start to find the coefficient in front of the first one (the only one which contains an x), then the second one, then the last one.

Then calculate the right side to know which number it should be equal to. If the combination of the first three equations and the fourth equation yield the same result, your sy

Answer 2

Step-by-step explanation:

Consider the two equations ax+by=c and dx+ey=f. Since these equations represent two lines in the xy-plane, the simultaneous solution of these two equations (i.e. those points (x,y) that satisfy both equations) is merely the intersection of the two lines. The graphs below illustrate the three possible cases: non-parallel lines, parallel (but not identical) lines, and identical lines.

From left to right these cases yield one solution, no solutions, and infinite solutions. The same situation occurs in three dimensions; the solution of 3 equations with 3 unknowns is the intersection of the 3 planes.

There is a simple tool for determining the number of solutions of a square system of equations: the determinant.