![]() To solve any system of two equations, we must reduce it to one equation in one of the unknowns. ![]() (Andre has twice as much as Bob, on the right - after Bob gives him $22.) "While if Bob gave Andre $22, Andre would then have twice as much (Andre - x - has the same amount as Bob, after he gives him $20.) "If Andre gave Bob $20, they would have the same amount." (In general, to have a unique solution, the number of equations must equal the number of unknowns.) How can we get two equations out of the given information? We must translate each verbal sentence into the language of algebra. Since there are two unknowns, there must be two equations. Let y be the amount that Bob has.Īlways let x and y answer the question - and be perfectly clear about what they represent! ![]() Let x be the amount of money that Andre has. While if Bob gave Andre $22, Andre would then have twice as much as Bob. If Andre gave Bob $20, they would have the same amount. H ERE ARE SOME EXAMPLES of problems that lead to simultaneous equations.Įxample 1.
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