How To Solve A Substitution Problem

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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.

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

In cases like this, you can use algebraic methods to find exact answers.

One method to look at is called the substitution method.In this case, there are an infinite number of solutions. Parallel lines have the same slope, but she also has to check whether they have different y-intercepts because the lines could be collinear (remember that 2 collinear lines are the same line).If Aubrey finds that the slopes of the lines are the same and the y-intercepts are different, then she can be confident that her answer is correct. The origin has no bearing on whether two lines are parallel.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.Remember that, when you're trying to solve a system, you're trying to use the second equation to narrow down the choices of points on the first equation.You're trying to find the one single point that works in both equations. We already knew, from the previous lesson, that this system was dependent, but now you know what the algebra looks like.But in a dependent system, the "second" equation is really just another copy of the first equation, and all the points on the one line will work in the other line." — something that's true, but unhelpful (I mean, duh! Neither of these equations is particularly easier than the other for solving.I'll get fractions, no matter which equation and which variable I choose. I guess I'll take the first equation, and I'll solve it for, um, Keep in mind that, when solving, you're trying to find where the lines intersect. Then you're going to get some kind of wrong answer when you assume that there is a solution (as I did when I tried to find that solution).You might ask yourself, "Why wouldn't I just want to graph the equations to find the solution? You may not have graph paper or an accurate way to graph the equations, thus making it hard to identify the solution.Or, as the equations become more difficult, the solution is not always an identifiable point on the graph.


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