Solving Systems of Two 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 is the point(s) where the equations intersect on a graph.

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How do you solve a system of linear equations using substitution?

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To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation to find 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 is the intersection point(s) of the lines representing each equation. If they intersect at one point, there is one solution; if they are parallel, there are no solutions; if they are the same line, there are infinitely many solutions.

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

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If two lines are parallel, it means that the system of equations has no solution, as the lines never intersect.

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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 solution to the system of equations 2x + y = 40 and x - 2y = -20?

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The solution is x = 12, y = 16.

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How can 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. If both equations are satisfied, the point is a solution.

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What is the significance of the coefficients in a linear equation?

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The coefficients represent the rate of change of the dependent variable with respect to the independent variable. They determine the slope of the line when graphed.

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How do you interpret the y-intercept in a linear equation?

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The y-intercept is the value of y when x = 0. It represents the point where the line crosses the y-axis.

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What is the meaning of the slope in a linear equation?

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The slope indicates the steepness of the line and the direction of the relationship between the variables. A positive slope means the line rises, while a negative slope means it falls.