# What is the formula for system of equations?

They are formed by two expressions that are equal to each other.

### If a system of equations is independent how many soultions will it have?

A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.

### What does solving a system of equations actually mean?

That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations. That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations. That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations. That means to…

### How does writing equivalent equations help you solve a system of equations?

You can write an equivalent equation from a selected equation in the system of equations to isolate a variable. You can then take that variable and substitute it into the other equations. Then you will have a system of equations with one less equation and one less variable and it will be simpler to solve.

### What is independent system?

Independence: The equations of a linear system are independent if none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set. Consistency: The equations of a linear system are consistent if they possess a common solution, and inconsistent otherwise. When the equations are inconsistent, it is possible to derive…

### What are the three types of systems of linear equations and their characteristics?

Independence: The equations of a linear system are independent if none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set. Consistency: The equations of a linear system are consistent if they possess a common solution, and inconsistent otherwise. When the equations are inconsistent, it is possible to derive…

### What are equations with the same solution?

Equations with the same solution are called dependent equations, which are equations that represent the same line; therefore every point on the line of a dependent equation represents a solution. Since there is an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 2x + y = 8 4x + 2y = 16 These equations are dependent. Since they represent the same line, all points that satisfy…