Unit 7 Review - Systems

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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What does it mean if a system of equations has no solution?

Back

A system of equations has no solution if the equations represent parallel lines that never intersect.

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How do you determine if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning they are dependent.

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What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = b, where b is the y-coordinate of any point on the line.

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How do you write the equation of a vertical line?

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The equation of a vertical line is of the form x = a, where a is the x-coordinate of any point on the line.

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What is the purpose of using a system of equations in real-life problems?

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Systems of equations are used to find the values of variables that satisfy multiple conditions or constraints simultaneously.

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What is the graphical representation of a system of inequalities?

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The graphical representation of a system of inequalities shows a shaded region that satisfies all inequalities, often bounded by lines.

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How do you solve a system of equations using substitution?

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To solve by substitution, solve one equation for one variable and substitute that expression into the other equation.

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What is the elimination method for solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for two equations to be independent?

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Two equations are independent if they represent lines that intersect at exactly one point, meaning they have one unique solution.