Solving Systems of Equations

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What is a system of equations?

Back

A set of two or more equations with the same variables.

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What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

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What is the graphical representation of a system of equations?

Back

The solution is the point where the graphs of the equations intersect.

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What is slope-intercept form?

Back

It is a way of writing linear equations in the form y = mx + b, where m is the slope and b is the y-intercept.

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How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

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

Back

It means the lines representing the equations are parallel and never intersect.

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What is the substitution method in solving systems of equations?

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It involves solving one equation for one variable and 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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It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point on a coordinate plane.

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How can you verify if an ordered pair is a solution to a system of equations?

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Substitute the x and y values into both equations; if both equations are true, it is a solution.