Writing System of Linear Equations

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What is a linear equation?

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A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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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 and the direction it goes (positive or negative).

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What is the y-intercept in a linear equation?

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The y-intercept is the point where the line crosses the y-axis. It is the value of y when x = 0.

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How do you write a system of equations?

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A system of equations is written as two or more equations that share the same variables. For example: 2x + 3y = 6 and x - y = 2.

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What is the solution to a system of equations?

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The solution to a system of equations is the point (or points) where the equations intersect on a graph, representing the values of the variables that satisfy all equations.

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What is substitution in solving systems of equations?

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Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

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What is elimination in solving systems of equations?

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Elimination is a method where you add or subtract equations to eliminate one variable, making it easier to solve for the other variable.

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What does it mean for a system of equations to be consistent?

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A consistent system of equations has at least one solution, meaning the lines intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system of equations has no solutions, meaning the lines are parallel and never intersect.

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What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.