How To Solve A Substitution Problem

Take note of how we have an equation with variables on both sides. Pay close attention to the very last step of the solution. Let's take a look at another example where you will find that you cannot solve the system.

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In this case, both equations are already solved for a variable; therefore, we can substitute one expression for y and solve! Since my x terms cancel out, we are left with 4 = -8. Can you imagine what type of graph this system represents? This is an example of what will happen if you are using the substitution method and there are no solutions. This also looks strange because again, 6x - 6x = 0. If it makes sense, you have an infinite number of solutions and if it doesn't make sense, then you have no solution.A graph can be used to show the solution for a system of two linear equations.However, accurately determining the solution from a graph is not always easy or accurate.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.For example, where do you think the two lines shown below intersect?It looks like they might intersect at (1.8, –0.7)—though this is only an estimate.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.Standardized Test Prep ACCUPLACER Math ACT Math ASVAB Math CBEST Math CHSPE Math CLEP Math COMPASS Math FTCE Math GED Math GMAT Math GRE Math MTEL Math NES Math PERT Math PRAXIS Math SAT Math TABE Math TEAS Math TSI Math more tests...The substitution method is one of two ways to solve systems of equations without graphing.


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