Flashcard - 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 to the system is the point(s) where the equations 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. This means that one line is the negative reciprocal of the other.

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How do you determine if a system of equations has no solution?

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A system has no solution if the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts.

Front

What is the slope-intercept form of a linear equation?

Back

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How can you graph a linear equation?

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To graph a linear equation, you can find two points that satisfy the equation and plot them on a coordinate plane, then draw a line through those points.

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What is the substitution method for 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 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 variable.

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What does it mean for a system of equations to have infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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How do you find the intersection point of two lines?

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To find the intersection point, solve the system of equations formed by the two lines to find the values of the variables at which they are equal.

Front

What is a linear equation?

Back