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 point(s) where the equations intersect.

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What does it mean for two equations to intersect on a graph?

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When two equations intersect on a graph, it means they have a common solution, which is the point where their graphs meet.

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How can you determine the solution to a system of equations graphically?

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You can determine the solution by graphing both equations on the same coordinate plane and identifying the point where they intersect.

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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.

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How do you convert an equation to slope-intercept form?

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To convert an equation to slope-intercept form, solve for y in terms of x, isolating y on one side of the equation.

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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 they have the same slope but different y-intercepts, indicating that they will never intersect and thus have no solution.

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What is the significance of the y-intercept in a linear equation?

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The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

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How can you represent a real-world situation using a system of equations?

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A real-world situation can be represented using a system of equations by defining variables for the quantities involved and creating equations based on relationships between those quantities.

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What is the method of substitution in solving systems of equations?

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The method of substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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What is the method of elimination in solving systems of equations?

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The method of elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.