System of Equations Flashcard

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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What does it mean to solve a system of equations using substitution?

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

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What is the graphical representation of a system of equations?

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The graphical representation is the intersection point(s) of the lines represented by the equations on a coordinate plane.

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

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No solution means that the lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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Infinitely many solutions occur when the equations represent the same line, meaning every point on the line is a solution.

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How do you determine if a system of equations has a unique solution?

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A unique solution exists if the lines intersect at exactly one point, indicating different slopes for the equations.

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What is the substitution method?

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The substitution method involves isolating one variable in one equation and substituting that expression into the other equation.

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What is the elimination method?

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

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How do you graph a linear equation?

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To graph a linear equation, find two or more points that satisfy the equation and plot them on a coordinate plane, then connect the points with a straight line.

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

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