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 graphically?

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Solving a system of equations graphically means plotting the equations on a graph and identifying the point(s) where they intersect, which represents the solution.

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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 determine if a system of equations has no solution?

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A system has no solution if the lines represented by the equations are parallel, meaning they never intersect.

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How do you determine if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

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

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

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What is a linear equation?

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A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

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What does the y-intercept represent 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 0.