Solving Systems of Linear Equations

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What is a system of linear equations?

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A set of two or more linear equations with the same variables.

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What does it mean to solve a system of linear equations?

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Finding the values of the variables that satisfy all equations in the system simultaneously.

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

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The intersection point(s) of the lines representing the equations on a graph.

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What is the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the elimination method in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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What does it mean if two lines are parallel in a system of equations?

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The system has no solution because the lines never intersect.

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What does it mean if two lines coincide in a system of equations?

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The system has infinitely many solutions because the lines are the same.

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How do you determine the solution of a system of equations graphically?

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By finding the point where the lines intersect on a graph.

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What is the y-intercept of a linear equation?

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The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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What is the slope of a linear equation?

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The rate of change of y with respect to x, represented as 'm' in the equation y = mx + b.