Solving Systems of Linear Equations by Graphing

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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 do you graph a linear equation in slope-intercept form?

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To graph a linear equation in slope-intercept form (y = mx + b), identify the y-intercept (b) and the slope (m). Start at the y-intercept on the y-axis, then use the slope to find another point.

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

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If two lines are parallel, it means they have the same slope but different y-intercepts. This indicates that the system has no solution, as the lines never intersect.

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What does it mean if two lines are coincident when graphing a system of linear equations?

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If two lines are coincident, they lie on top of each other, meaning they have the same slope and y-intercept. This indicates that there are infinitely many solutions to the system.

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

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The graphical representation of a solution to a system of linear equations is the point(s) where the lines intersect on the graph.

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How can you determine if a system of linear equations has one solution, no solution, or infinitely many solutions?

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You can determine this by graphing the equations: one solution occurs when the lines intersect at one point, no solution occurs when the lines are parallel, and infinitely many solutions occur when the lines are coincident.

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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 to find the values of both variables.

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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 significance of the point of intersection in a system of linear equations?

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The point of intersection represents the solution to the system, indicating the values of the variables that satisfy all equations in the system.

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How do you convert a linear equation from standard form to slope-intercept form?

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To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y by isolating it on one side of the equation.