Semester 1 Algebra Test

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What is a linear equation?

Back

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 it mean if a system of equations has one solution?

Back

It means that the two lines represented by the equations intersect at exactly one point.

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What does it mean if a system of equations has infinitely many solutions?

Back

It means that the two lines represented by the equations are coincident, meaning they lie on top of each other.

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What does it mean if a system of equations has no solution?

Back

It means that the two lines represented by the equations are parallel and will 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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What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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What is the graphical method of solving systems of equations?

Back

The graphical method involves graphing both equations on the same set of axes and identifying the point(s) of intersection.

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What are coincident lines?

Back

Coincident lines are lines that lie on top of each other, representing infinitely many solutions to a system of equations.

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What are parallel lines?

Back

Parallel lines are lines that never intersect, representing no solutions to a system of equations.

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What is the slope of a line?

Back

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