How do you solve 3 sets of simultaneous equations?
Table of Contents
How do you solve 3 sets of simultaneous equations?
Pick any two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. Solve the system of the two new equations using the Addition/Subtraction method. Substitute the solution back into one of the original equations and solve for the third variable.
Is it possible for a system of three linear equations and three unknowns to have exactly three solutions justify?
Yes, they can have more than one solution. Each equation α⋅x=β describes an affine plane. If 2 of your 3 planes are identical (and different from the 3rd), then the intersection might be a line, thus infinite many solutions, or is empty in case of parallel planes.
Is it possible for a linear system to have exactly 3 solutions?
It is possible for a linear system of equations to have exactly three solutions.
How many solutions can a system of three equations with three variables have?
infinite number
For systems of equations in three variables, there are an infinite number of solutions on a line or plane that is the intersection of three planes in space.
Can a system of 3 equations have 2 solutions?
Most linear systems you will encounter will have exactly one solution. However, it is possible that there are no solutions, or infinitely many. (It is not possible that there are exactly two solutions.) The word unique in this context means there is a solution, and it’s the only one.
How many solutions does a system of three equations have?
infinite
Case 3: There are an infinite number of solutions. This occurs when the three planes intersect in a line. And this can also occur when the three equations graph as the same plane.
What makes a system of three equations with three variables inconsistent?
Systems of equations in three variables that are inconsistent could result from three parallel planes, two parallel planes and one intersecting plane, or three planes that intersect the other two but not at the same location.
