Solving Systems of Linear Equations in Two Variables

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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.

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What does it mean to solve a system of linear equations graphically?

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Solving a system of linear equations graphically involves plotting the equations on a coordinate plane and identifying the point(s) where the lines intersect, which represents the solution.

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What is the elimination method for solving systems of linear 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 substitution method for solving systems of linear 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 significance of the solution (0, 5) in the context of a system of equations?

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The solution (0, 5) indicates that when x = 0, y = 5 satisfies both equations in the system.

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

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A system of equations has no solution if the lines represented by the equations are parallel, meaning they never intersect.

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

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A system of equations 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 role of coefficients in a linear equation?

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Coefficients are the numerical factors that multiply the variables in a linear equation, determining the slope and position of the line.

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How can you use multiplication to solve a system of equations?

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You can multiply one or both equations by a number to create equivalent equations that can be solved more easily, often used in the elimination method.

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What is the graphical representation of the equation y = 4x + 1?

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The equation y = 4x + 1 represents a straight line with a slope of 4 and a y-intercept of 1.