Solving Systems of Equations

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What is a system of equations?

Back

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 for a system of equations to have one solution?

Back

A system has one solution when the graphs of the equations intersect at exactly one point.

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What does it mean for a system of equations to have no solution?

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A system has no solution when the equations represent parallel lines that never intersect.

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What does it mean for a system of equations to have infinitely many solutions?

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A system has infinitely many solutions when the equations represent the same line, meaning they intersect at every point on that line.

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

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You can determine the solution by graphing the equations and identifying the point(s) where the lines intersect.

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What is the substitution method for 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 for 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 other variable.

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How do you write a system of equations from a word problem?

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Identify the variables, translate the relationships and conditions into equations, and write them as a system.

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What is the significance of the coefficients in a system of equations?

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Coefficients represent the rate of change of the variables and affect the slope of the lines in the graph.

Front

What is the graphical representation of the equation y = mx + b?

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This equation represents a straight line where 'm' is the slope and 'b' is the y-intercept.