# Write a system of equations given the graph express

The applications for systems seems almost endless, but we will just show one more. Graphically, an infinite number of solutions represents a line or coincident plane that serves as the intersection of three planes in space.

You want to keep it as simple as possible.

### How to write a system of equations with a given solution

Solve Systems of Three Equations in Three Variables In order to solve systems of equations in three variables, known as three-by-three systems, the primary goal is to eliminate one variable at a time to achieve back-substitution. Authored by: James Sousa Mathispower4u. Clearly, knowing the quantity for which the cost equals the revenue is of great importance to businesses. However, the graph of a system of equations can still give a good idea of what type of solution, if any, exists. Therefore, the system has no solution. If a variable already has opposite coefficients than go right to adding the two equations together. Check it in the other equation. The number of 2-point shots she made was one greater than the number of 3-point shots she made. B Correct. To make a profit, the business must produce and sell more than 50, units. The area to the left of the break-even point represents operating at a loss.

Try It Solve the system of equations in three variables. These two lines cannot intersect twice. We can use this to write an equation for the revenue. A system of equations in three variables is dependent if it has an infinite number of solutions. Find the solution by setting the two linear functions equal to another and solving for x, or find the point of intersection on a graph. Since these two lines are not identical, the system will not have an infinite number of solutions.

However, finding solutions to systems of three equations requires a bit more organization and a touch of visual gymnastics.

### No solution graph

Authored by: Roy Shahbazian. D Incorrect. Graphically, the ordered triple defines a point that is the intersection of three planes in space. Example: Finding the Solution to a Dependent System of Equations Find the solution to the given system of three equations in three variables. Plotting both equations, it looks like there is no solution—the lines are parallel. Solve the following system of equations in two variables. You can write up your answer by writing out either equation to indicate that they are the same equation. Try It Classify Solutions to Systems in Three Variables Just as with systems of equations in two variables, we may come across an inconsistent system of equations in three variables, which means that it does not have a solution that satisfies all three equations.

A system of equations in three variables is inconsistent if no solution exists. Below, we summarize three key factors that will help guide you in translating a situation into a system. Look at the images below. The cost function is the function used to calculate the costs of doing business. Check it in the other equation.

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