To solve systems using substitution, follow this procedure.
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Select one equation and solve for one of its variables.
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In the other equation, substitute for the variable just solved.
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Solve the new equation.
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Substitute the value found into any equation involving both variables and solve for the other variable.
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Check the solution in both original equations.
Example 1: Solve this system of equations by using substitution.
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Solve for
x.
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Substitute
for
x in the other equation.
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Solve this new equation.
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Substitute into any equation involving both variables.
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Check the solution in both original equations.
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The solution is x = 1, y = –2.
If the substitution method produces a sentence that is always true, such as 0 = 0, then the system is dependent, and either original equation is a solution. If the substitution method produces a sentence that is always false, such as 0 = 5, then the system is inconsistent, and there is no solution.












Linear Sentences in One Variable
Linear Sentences In Two Variables


