Systems of Equations - Algebra I Honors 2024

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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 if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

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What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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

Back

If the equations represent the same line, they have infinitely many solutions.

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What is the graphical representation of a system of equations?

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The graphical representation is the intersection points of the lines on a coordinate plane.

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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 other.

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

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Identify the variables, translate the relationships into equations, and ensure you have as many equations as variables.

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What does it mean for two equations to be dependent?

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Dependent equations are equations that represent the same line, leading to infinitely many solutions.

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

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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How do you find the intersection of two lines algebraically?

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Set the equations equal to each other and solve for the variable, then substitute back to find the other variable.