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And you could try it out on both of these equations right here. So let's verify that it also satisfies this bottom equation. 5 times 7/2 is 35 over 2 minus 4 times negative 2, so minus negative 8. That's equivalent to-- let's see, this is 17.5 plus 8. And that indeed does equal 25.5. So this satisfies both equations.If we multiply the second equation in System B by 3 , we get: 3 x − 4 y = 2 3 ( 3 x − 4 y) = 3 ( 2) 9 x − 12 y = 6. Replacing the second equation of System B with this new equation, we get an equivalent system: − 12 x + 9 y = 7 9 x − 12 y = 6. Whoa! Look at that! This system is the same as System A, which means system A is equivalent ...OpenStax. In this chapter, we will investigate matrices and their inverses, and various ways to use matrices to solve systems of equations. 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This unit begins by ensuring that students understand that solutions to equations are points that make the equation true, while solutions to systems make all equations (or inequalities) true. Graphical and substitution methods for solving systems are reviewed before the development of the ... System of Linear Inequalities. two or more iequalities. System of Equations. a set of two or more equations containing the same variables. Solution. ordered pair that makes both equations trues in a system of equations. Point of Intersection. The point where two lines cross. Represents the solution to a system of equations.Unit 5 systems of equations & inequalities
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