Solving Systems of Equations

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

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How do you solve a system of equations graphically?

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To solve a system of equations graphically, you plot each equation on the same coordinate plane and identify the point(s) where the lines intersect. This point(s) represents the solution(s) to the system.

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What does it mean 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 and never intersect. This indicates that there are no values that satisfy both equations.

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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 to the system.

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What is the substitution method for solving systems of equations?

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The substitution method involves solving one of the equations 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 the equations to eliminate one variable, making it easier to solve for the remaining variable.

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How do you write a system of equations from a word problem?

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To write a system of equations from a word problem, identify the variables, translate the relationships and conditions described in the problem into equations, and ensure they represent the same situation.

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What is the significance of the point of intersection in a system of equations?

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

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How can you determine if two lines are parallel from their equations?

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Two lines are parallel if they have the same slope but different y-intercepts. In slope-intercept form (y = mx + b), if the values of m are equal and b is different, the lines are parallel.

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What is slope-intercept form of a linear equation?

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The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.