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Systems of Equations
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A system of equations is a set of equations that have the same variables. A solution for the system is an assignment of variables that make each equation true. To solve a system we find all possible solutions. "Je reconnais devoir beaucoup aux lumières de MM. Bernoulli, surtout à celles du jeune (Jean) présentement professeur à Groningue. Je me suis servi sans façon de leurs découvertes et de celles de M. Leibniz. C'est pourquoi je consens qu'ils en revendiquent tout ce qu'il leur plaira, me contentant de ce qu'ils voudront bien me laisser." "I recognize I owe much to Messrs. Bernoulli's insights, above all to the young (John), currently a professor in Groningue. I did unceremoniously use their discoveries, as well as those of Mr. Leibniz. For this reason I consent that they claim as much credit as they please, and will content myself with what they will agree to leave me."
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Solving by Substitution (1) Solve for one variable: Pick one of the equations and solve for one variable in terms of the other variable. (2) Substitute: Substitute the expression you found above into the other equation to get an equation in one variable. Then solve for that variable. (3) Back Substitute. Substitute the answer from (2) above into the expression found in Step (1) and then solve for the remaining variable.
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