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Unit 4 Systems of Equations and Inequalities Lesson 19 Graphing to Solve Systems of EquationsNAME:PERIOD:DATE:Homework Problem Set Solve each system by graphing, and then check your answer. 1.y !
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To fill out systems of equations, follow these steps:
02
Write down the equations. Make sure that the variables in each equation match up.
03
Choose a method to solve the system of equations, such as substitution, elimination, or graphing.
04
If using substitution, solve one equation for one variable and substitute the expression into the other equation.
05
If using elimination, multiply one or both equations by a constant so that the coefficients agree on one variable and add or subtract the equations to eliminate that variable.
06
If using graphing, plot the equations on a graph and find the point of intersection or where the lines are parallel.
07
Solve for the remaining variables by substituting the value of one variable into the other equation(s).
08
Check that the solution satisfies all the original equations.

Who needs systems of equations and?

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Students studying algebra or linear equations need systems of equations.
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Engineers and scientists often use systems of equations to model and solve real-world problems.
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Economists may use systems of equations to analyze supply and demand, production, and other economic phenomena.
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Anyone interested in solving multiple related equations simultaneously can benefit from using systems of equations.
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A system of equations is a collection of two or more equations with a same set of variables. The solution to the system is the set of values that satisfy all equations simultaneously.
Individuals and entities involved in certain financial activities, such as partnerships or corporations, are typically required to file systems of equations, as they must report their collective income, deductions, and tax liabilities.
To fill out systems of equations, gather necessary financial data, ensure each variable is accounted for, substitute known values into the equations, and solve for unknowns using methods like substitution or elimination.
The purpose of systems of equations is to analyze and solve problems involving multiple variables, allowing for comprehensive insights into complex relationships or scenarios.
Commonly reported information includes income figures, expenses, tax deductions, credits, and any other relevant financial data pertinent to the entities involved.
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