Replace one coefficient column at a time and divide determinants to find x and y when the coefficient determinant is nonzero.
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You know already how to solve systems of linear equations using substitution, elimination, and graphing. This time, we want to talk about how to solve systems using inverse matrices.
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We know already how to solve systems of linear equations using substitution, elimination, and graphing. This time, we want to talk about how to solve systems using inverse matrices. To walk through this, let’s use a simple system.
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In math and science you might meet a variable with a subscript. Don’t let them scare you, they’re just a way to keep track of variables that could be related to each other in some way. For instance, if we’re doing a problem involving the distance that two people travel, we might use the variables D_A and D_B to indicate the distances related to person A and person B, respectively.
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Age word problems are like number word problems. You’ll still need to relate sentences in English to mathematical equations to solve for people’s ages. In this lesson we’ll look at how to do that. One helpful way to organize these types of problems is by making a table.
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Eliminate one variable twice, solve the resulting two-equation system, and substitute back. See how elimination also reveals an inconsistent system.
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Choose substitution, elimination, or graphing to solve a linear system. Follow worked examples and compare the exact solution with its graph.
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