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 is the point(s) where the equations intersect.

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What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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What is the substitution method in 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.

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What is the elimination method in 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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How do you graph a linear equation?

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To graph a linear equation, find two or more points that satisfy the equation and plot them on a coordinate plane, then draw a line through the points.

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What is the slope-intercept form of a linear equation?

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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 y with respect to x; it indicates how steep the line is.

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What is the y-intercept of a linear equation?

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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 satisfied, the point is a solution.

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What is an inequality in the context of systems of equations?

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An inequality is a mathematical statement that compares two expressions, indicating that one is greater than, less than, or equal to the other.