Substitution is a way to solve without graphing, and sometimes there are equations that are impossible or very difficult to graph that are easier to just substitute. Mostly though, it is a way to solve if you have no calculator or cannot use one (for a test or worksheet).
The solution is the coordinates of the point where the graphs of the equations intersect.
Simultaneous equations can also be solved by substitution or graphically
When solving a system of equations by graphing, you will need to graph the equations on the same coordinate plane. This allows you to visually identify the point where the two lines intersect, which represents the solution to the system. If the lines intersect at a single point, that point is the unique solution; if the lines are parallel, there is no solution; and if they coincide, there are infinitely many solutions.
The two methods of intersection typically refer to geometric and algebraic approaches. The geometric method involves graphing the equations and visually identifying the points where they intersect. The algebraic method involves solving the equations simultaneously, either by substitution or elimination, to find the exact coordinates of the intersection points. Each method has its advantages depending on the context and complexity of the equations involved.
You use substitution when you can solve for one variable in terms of the others. By substituting, you remove one variable from the equation, which can then be solved. Once you solve for one variable, you can use substitution to find the other.
There are no disadvantages. There are three main ways to solve linear equations which are: substitution, graphing, and elimination. The method that is most appropriate can be found by looking at the equation.
In systems of equations, the graphing method is solving x and y by graphing out the two equations. x and y being the coordinates of the two line's intersection.
The solution is the coordinates of the point where the graphs of the equations intersect.
The advantage of solving a system of linear equations by graphing is that it is relatively easy to do and requires very little algebra. The main disadvantage is that your answer will be approximate due to having to read the answer from a graph. Where the solution are integer values, this might be alright, but if you are looking for an accurate decimal answer, this might not be able to be achieved. Another disadvantage to solving linear equations by graphing is that at most you can have two unknown variables (assuming that you are drawing the graph by hand).
By substitution or elimination in simultaneous equations.
The first step is to show the equations which have not been shown.
Graphing
Simultaneous equations can also be solved by substitution or graphically
Isolating a variable in one of the equations.
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you cannot determine the exact value of the point
The first step is to solve one of the equations for one of the variables. This is then substituted into the other equation or equations.