Often times when solving a real-world application, more than one equation is necessary to describe the information. We’ll investigate some of those in this section.
Admission into a carnival for children and adults is . For children and adults, the admission is . Assuming a different price for children and adults, what is the price of the child’s admission and the price of the adult admission?
Let represent the cost of a child’s admission and the cost of an adult admission. Write an equation to represent the total cost for children and adults.
A system of linear equations consists of two or more linear equations made up of two or more variables. A solution to a system of equations is a value for each of the variables that satisfies all the equations at the same time.
While we can test points to determine if they are solutions, it is not feasible to test every possible point to find a solution. We need a method to solve a system.
Sometimes it is difficult to determine the exact intersection point of two lines using a graph. Let’s explore another possible method for solving a system of equations.
While the substitution method will always work, sometimes the resulting equations will be difficult to solve. Let’s explore a third method for solving a system of two linear equations with two variables.
Notice that if you simply add the two equations together, it will not eliminate a variable. Substitution will also be difficult since it involves fractions.