How do you solve systems of linear equations using substitution or elimination?

Solving systems of linear equations is a fundamental topic in algebra, and there are two main methods used to solve them: substitution and elimination. In this answer, we will discuss these methods and their applications.

Substitution Method

The substitution method is the simpler of the two methods, and it involves solving one of the equations for one of the variables, and then plugging that expression into the other equation to solve for the other variable. The steps to use the substitution method are:

• Solve one of the equations for one of the variables.
• Substitute the expression obtained in step 1 into the other equation.
• Solve the resulting equation for the remaining variable.
• Substitute the value obtained in step 3 into either of the original equations to find the value of the other variable.

Elimination Method

The elimination method is slightly more complicated than the substitution method, but it is often faster for solving systems of linear equations. This method involves adding or subtracting the equations to eliminate one of the variables, and then solving for the other variable. The steps to use the elimination method are:

• Multiply one or both of the equations by constants to obtain coefficients that are opposites for one of the variables.
• Add or subtract the equations to eliminate one of the variables.
• Solve the resulting equation for the remaining variable.
• Substitute the value obtained in step 3 into either of the original equations to find the value of the other variable.

Both methods are useful for solving systems of linear equations, and the choice of which method to use depends on the specific problem at hand. Substitution method is easier to understand, but can be time-consuming for larger systems, whereas the elimination method can be faster but requires more work to set up.