Systems of equations

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

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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. It can be either a unique solution or infinitely many solutions.

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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 equations represent parallel lines that never intersect.

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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 point(s) of the lines represented by the equations on a coordinate plane.

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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.

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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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How do you determine if two lines are parallel?

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Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

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

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The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

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What is the point of intersection of two lines?

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

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How can you check the solution of a system of equations?

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You can check the solution by substituting the values back into the original equations to see if they hold true.