S.R said:
EDIT: The mistake is 7/3; it is suppose to be 10/3.Mark44 said:
Mark44 said:
.Systems of equations are a set of equations with multiple variables that are solved simultaneously to find the values of each variable. They are used to model real-world situations and can have one or more solutions.
Word problems involve real-world scenarios that can be modeled using systems of equations. By setting up and solving the equations, we can find the values of the variables that represent the unknown quantities in the problem.
A consistent system of equations has at least one solution, meaning the graphs of the equations intersect at a point. An inconsistent system has no solution, meaning the graphs are parallel and never intersect.
If one of the equations has a variable with a coefficient of 1 or -1, substitution may be the best method. If the coefficients of one variable in both equations are the same or opposite, elimination may be the best method. It is also helpful to consider the number of variables and equations in the system.
Systems of equations can be used to solve many types of word problems, but not all. They are most commonly used for problems involving two or three unknown quantities that can be represented by two or three equations. If the problem has more than three unknown quantities, it may be more efficient to use other methods such as matrices or linear programming.