## Solving Problems

There are three ways to solve a system of equations using the algebraic method. The first is by graphing the two equations. You will find the solution at the intersection of the two lines. The second way involves rearrangement of the equations and substituting one variable’s value for the other. The third method is by solving the system using the substitution method. All the methods involve the use of a graphing calculator.

An example of a word problem is a math problem written as a story, which requires you to visualize the solution. You have probably encountered and solved word problems in math class. For example, in “Jack has twelve apples” you will find that Johnny has eight apples left over after giving four to Susie. Algebraic word problems are more complex, but use the same basic **solving problems algebraically** techniques that you learn in lower-level mathematics.

Another way to solve a problem algebraically is to graph the variables. A numerical expression is made up of numbers alone, and does not include variables. An algebraic expression, however, contains variables along with the numbers. By arranging these variables side-by-side in an equation, you make it easier to find solutions to unknown terms. You need to place the variables on one side of the equation, and the constants on the other. You can also separate the variables by performing arithmetic operations on them.

## Solving Problems Algebraically

In addition to graphing the solutions, you can use the graphing utility to check the accuracy of your solutions. When you are doing this, you can also make an approximate solution, and compare it with the original. This will allow you to make sure that the solutions are the same. If you are unsure about the solution, you can always substitute a value into the original equation to confirm its accuracy. If you have a problem with a radical, use the substitution method.

In addition to using the elimination method, you can also use the substitution method. The substitution method uses a variable in the original equation to replace it with another. The resulting equations are interchangeable and can be checked by examining the RHS of the equations. If a term is not equal to a constant, then you must use it to make the same answer. This is the only way to ensure that a given solution is equivalent to the other.

When two or more equations are related, they can be solved by adding them. If one of the variables is greater than the other, you can use the substitution method. In a similar way, the substitution method allows you to use one variable to solve the other. When you find a solution to a system of equations, you can simplify it further. Once you have the solution, you can start analyzing the system of equations and evaluate the final solution.