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 in the system.

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What does it mean to solve a system of equations using elimination?

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Solving a system of equations using elimination involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the remaining variable.

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What is the solution to the system of equations 2x - 3y = 6 and 7x - 3y = -9?

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The solution is (-3, -4).

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What does it mean if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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What is the solution to the system of equations 2x + y = 5 and x - y = -2?

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The solution is (1, 3).

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What is the significance of the slopes of parallel lines in a system of equations?

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The slopes of parallel lines are the same, indicating that the lines never intersect and thus have no solutions.

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How can you determine if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines, which have the same slope but different y-intercepts.

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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.

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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 substituting that expression into the other equation.

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What is the difference between consistent and inconsistent systems of equations?

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A consistent system has at least one solution, while an inconsistent system has no solutions.