Solution to a Graphed System of Linear Equations

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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 to the system is the point(s) where the equations intersect on a graph.

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How can you graph a system of linear equations?

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To graph a system of linear equations, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect.

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What does it mean if two lines intersect at a point?

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If two lines intersect at a point, it means that there is a unique solution to the system of equations represented by those lines.

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What does it mean if two lines are parallel?

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If two lines are parallel, it means they have the same slope and will never intersect, indicating that there is no solution to the system of equations.

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What does it mean if two lines coincide?

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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 of equations.

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How do you find the solution to a system of linear equations graphically?

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To find the solution graphically, plot both equations on the same graph and identify the coordinates of the intersection point.

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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 to find the values of both variables.

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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 solution (1, 3) in a system of equations?

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The solution (1, 3) indicates that when x = 1 and y = 3, both equations in the system are satisfied.

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How can you verify the solution to a system of equations?

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To verify the solution, substitute the values of the solution into both equations to check if they hold true.