Condition for Unique Solution to Linear Equations A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. i.e., if the two lines are neither parallel nor coincident.
For a given pair of linear equations in two variables, the graph is represented by two lines. If the lines intersect at a point, that point gives the unique solution for the two equations. If there is a unique solution of the given pair of equations, the equations are called consistent.
The case of a unique solution If the augmented matrix does not tell us there is no solution and if there is no free variable (i.e. every column other than the right-most column is a pivot column), then the system has a unique solution.
The graphical method of solving a system of equations in three variables involves plotting the planes that are formed when graphing each equation in the system and then finding the intersection point of all three planes. The single point where all three planes intersect is the unique solution to the system.
Originally Answered: When can you solve 3 variables in 2 equations? If we have a 2 x 3 coeifficient matrix, we have 2 equations and 3 variables. It is simply impossible to have 3 basic variables - a maximum of 2 are allowed. So, assuming we have a 2 basic variables, we have 1 free variable.
0:0315:26Solving 3 Equations with 3 Unknowns - YouTubeYouTube
Once a professor taught me a very important rule: When you have n unknowns, you need at least n equations to solve for all of them. You have four equations and four unknowns, so I expect that you'll be able to find the solution using regular "simultaneous equation" solving methods, such as substitution and elimination.
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How Much Gallon Bucket Of Water Weigh. 5 Gallons of pure water weighs 42.7 pounds because all gallon of water equals 8.35 pounds.