Systems of Equations

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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 for a system of equations to have no solution?

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A system has no solution if the lines represented by the equations are parallel and never intersect.

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

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A system has infinite solutions if the equations represent the same line, meaning they intersect at every point on that line.

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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, then substitute that expression into the other equation.

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How do you solve a system of equations using elimination?

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To solve by elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the other.

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What is the graphical representation of a system of equations?

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The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s).

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What is the point of intersection in a system of equations?

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The point of intersection is the solution to the system, representing the values of the variables that satisfy all equations.

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If a system of equations has one solution, what does that indicate about the lines?

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If there is one solution, the lines intersect at exactly one point, indicating they have different slopes.

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What is the standard form of a linear equation?

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

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