Unit 4 Systems of Equations Review

Front

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

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

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

Back

A system has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

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How do you solve a system of equations by substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

How do you solve a system of equations by elimination?

Back

To solve by elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines on a coordinate plane, which represent the solutions.

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What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, written as (x, y).

Front

How can you check if your solution to a system of equations is correct?

Back

You can check by substituting the ordered pair back into the original equations to see if both equations are satisfied.

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

Back

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

Front

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

Back

The slope indicates the steepness of the line and the direction it goes; a positive slope rises, while a negative slope falls.