Matching Graphs and 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 on a graph.

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What does it mean for two lines to be parallel in a system of equations?

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Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect and have no solution.

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What does it mean for two lines to be coincident in a system of equations?

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Two lines are coincident if they lie on top of each other, meaning they have infinitely many solutions as every point on the line is a solution.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations is the intersection points of the lines represented by the equations on a coordinate plane.

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How do you determine the solution of a system of equations graphically?

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The solution of a system of equations can be determined graphically by finding the point(s) where the lines intersect.

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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 other variable.

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

Back

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What is the point of intersection of two lines?

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The point of intersection is the coordinate point where two lines meet, representing the solution to the system of equations.

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

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A system of equations has no solution if the lines are parallel and do not intersect.