Solving 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 simultaneously.

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What does it mean for two lines to intersect?

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Two lines intersect when they cross each other at a point, which represents the solution to the system of equations formed by the two lines.

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How can you determine the solution to a system of equations graphically?

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The solution can be found by graphing both equations on the same coordinate plane and identifying the point where the two lines intersect.

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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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What is the significance of the point (1, -1) in a system of equations?

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The point (1, -1) is a solution to a system of equations, meaning that when x=1 and y=-1, both equations in the system are satisfied.

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How do you check if a point is a solution to a system of equations?

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To check if a point is a solution, substitute the x and y values of the point into both equations. If both equations are true, the point is a solution.

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What does it mean if two lines are parallel in the context of systems of equations?

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If two lines are parallel, they have the same slope but different y-intercepts, meaning they will never intersect and the system has no solution.

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What is the solution to the system of equations y = 8x + 1 and y = 6x + 3?

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The solution is (1, 9), which is the point where the two lines intersect.

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What is the meaning of the coordinates (4, -2) in a system of equations?

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The coordinates (4, -2) represent the point of intersection of two lines, indicating the solution to the system of equations.