Systems of Linear Equations (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 is the point(s) where the equations intersect.

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

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A solution is valid if it satisfies all equations in the system, making them true when the values are substituted.

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How is a solution to a system of linear equations represented?

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A solution is represented as an ordered pair (x, y), where x is the value of the first variable and y is the value of the second variable.

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What is the graphical representation of a system of linear equations?

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The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) to the system.

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What is the substitution method in solving systems of linear 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 elimination method in 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 other.

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

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If two lines are parallel, the system has no solution because the lines never intersect.

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

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If two lines coincide, the system has infinitely many solutions because every point on the line is a solution.

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What is the slope-intercept form of a linear equation?

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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How do you find the x-intercept of a linear equation?

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To find the x-intercept, set y = 0 in the equation and solve for x.