A.EI.2a:Application of 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 is the point(s) where the equations intersect on a graph.

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How do you represent a linear equation in two variables?

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What does the slope of a line represent?

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The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

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What is the y-intercept of a line?

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How can you solve a system of equations graphically?

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To solve a system of equations graphically, plot each equation on the same graph and identify the point(s) where the lines intersect. This point(s) is the solution.

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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 does it mean for an ordered pair to be a solution to a system of equations?

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An ordered pair (x, y) is a solution to a system of equations if it satisfies all equations in the system when substituted for x and y.

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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. If both equations are true, the point is a solution.

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What is the significance of parallel lines in a system of equations?

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Parallel lines in a system of equations indicate that there is no solution, as the lines never intersect.