Solving Systems of Linear Equations using Desmos

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

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How can you graphically solve a system of linear equations?

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You can graphically solve a system of linear equations by plotting each equation on the same coordinate plane and identifying the point(s) where the lines intersect.

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What does it mean for a point to be a solution to a system of equations?

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A point is a solution to a system of equations if it satisfies all equations in the system, meaning it makes all equations true when substituted.

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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 intersection point in a system of linear equations?

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The intersection point represents the solution to the system, indicating the values of the variables that satisfy all equations.

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

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To determine if a point is a solution, substitute the x and y values of the point into each equation and check if both equations are satisfied.

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

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If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

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What does it mean if two lines coincide in the context of a system of equations?

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

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What is the role of Desmos in solving systems of linear equations?

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Desmos is an online graphing calculator that allows users to graph equations and visually analyze the solutions to systems of linear equations.