Unit 4 Test Review: Systems of Equations

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What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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

Back

It means to find the point(s) where the graphs of the equations intersect, which represents the solution(s) to the system.

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What is the substitution method in solving systems of equations?

Back

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

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What is the elimination method in solving systems of equations?

Back

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?

Back

It means there is no solution to the system, as the lines never intersect.

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

Back

It means there are infinitely many solutions, as the lines are the same.

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How do you determine the solution of a system of equations from a graph?

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The solution is the coordinates of the point where the two lines intersect.

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What is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form y = mx + b.

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What is the meaning of the slope in a linear equation?

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The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

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What is the y-intercept in a linear equation?

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The y-intercept (b) is the point where the line crosses the y-axis, represented as (0, b).