*We have another example where the original system of equations is easily solved by using substitution. That means that there is NO SOLUTION to this system of equations. They will never intersect; therefore, there are no solutions. Every point on the line is a solution to the system. So, if you are solving a system algebraically and your variables cancel, you will need to see if your end statement makes sense.*

*We have another example where the original system of equations is easily solved by using substitution. That means that there is NO SOLUTION to this system of equations. They will never intersect; therefore, there are no solutions. Every point on the line is a solution to the system. So, if you are solving a system algebraically and your variables cancel, you will need to see if your end statement makes sense.*

The important thing here is that you are always substituting values that are equivalent.

If you solved the problem like that, you used a simple substitution—you substituted in the value “7” for “his daughter’s age.” You learned in the second part of the problem that “his daughter is 7.” So substituting in a value of “7” for “his daughter’s age” in the first part of the problem was okay, because you knew these two quantities were equal.

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The substitution method is one of two ways to solve systems of equations without graphing.

This means that the solution may contain decimals or fractions, which is not easy to identify on a graph.

Once you learn the algebraic method for solving a system of equations, you will probably find that it becomes your preferred method. The good news is that there are two methods, which makes this process easier depending on the problems you are given. The following steps can be used as a guide as you read through the examples for using the substitution method. Since this is a true statement, there are solutions and this happens to be an infinite number of solutions. These are the exact same line and that's why it's an infinite number of solutions.We knew, from the previous lesson, that this system represents two parallel lines.But I tried, by substitution, to find the intersection point anyway. Since there wasn't any intersection point, my attempt led to utter nonsense."), just as two identical lines are quite different from two parallel lines. A useless result means a dependent system which has a solution (the whole line); a nonsense result means an inconsistent system which has no solution of any kind.We know what this looks like graphically: we get two identical line equations, and a graph with just one line displayed. I did substitute the first equation into the second equation, so this unhelpful result is not because of some screw-up on my part.It's just that this is what a dependent system looks like when you try to find a solution.The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. The idea here is to solve one of the equations for one of the variables, and plug this into the other equation.It does not matter which equation or which variable you pick.In cases like this, you can use algebraic methods to find exact answers.One method to look at is called the substitution method.This system consists of two equations that both represent the same line; the two lines are collinear.Every point along the line will be a solution to the system, and that’s why the substitution method yields a true statement.

## Comments How To Solve A Substitution Problem

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