Writing Systems of Equations

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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 to solve a system of equations?

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To solve a system of equations means to find the values of the variables that make all equations true simultaneously.

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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What is the elimination method in 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 remaining variable.

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What is a linear equation?

Back

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the rise over run, or the change in y divided by the change in x.

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What does it mean for two lines to be parallel?

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Two lines are parallel if they have the same slope and will never intersect.

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What does it mean for two lines to be perpendicular?

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Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

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

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the same situation.

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What is the importance of the coefficients in a system of equations?

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Coefficients determine the relationship between the variables in the equations and affect the slope and position of the lines when graphed.