Writing Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations in the system.

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How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution in common.

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What does it mean for two equations to be independent?

Back

Two equations are independent if they represent different lines that intersect at exactly one point.

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What does it mean for two equations to be dependent?

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Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.

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How can you solve a system of equations graphically?

Back

By graphing each equation on the same coordinate plane and identifying the point(s) where the lines intersect.

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What is substitution in solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

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What is elimination in solving systems of equations?

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Elimination is a method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

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What is the importance of checking your solution in a system of equations?

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Checking your solution ensures that the values satisfy all equations in the system, confirming that the solution is correct.

Front

How do you write an equation from a word problem involving ages?

Back

Identify the ages as variables, express relationships using algebraic expressions, and set up an equation based on the total or difference given.