Systems of Equations (Graphs)

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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 on a graph.

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What does it mean for a system of equations to be consistent?

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A consistent system of equations has at least one solution, meaning the graphs of the equations intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system of equations has no solutions, meaning the graphs of the equations do not intersect at any point.

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What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, meaning the equations represent the same line on a graph.

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How can you determine the number of solutions in a system of equations by graphing?

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By graphing the equations, you can determine the number of solutions based on the intersection points: one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line).

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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 to find the solution.

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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 remaining variable.

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What is the graphical representation of a linear equation?

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The graphical representation of a linear equation is a straight line on a coordinate plane, where each point on the line represents a solution to the equation.

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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 (change in y) over the run (change in x). It indicates how much y changes for a given change in x.

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What is the y-intercept of a line?

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The y-intercept of a line is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.