Solving 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 substitution in solving systems of equations?

Back

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

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What is elimination in solving systems of equations?

Back

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

Front

What is the solution to a system of equations?

Back

The values of the variables that make all equations in the system true.

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How do you check if a solution is correct for a system of equations?

Back

Substitute the solution values back into the original equations to see if they hold true.

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What is interval notation?

Back

A way of writing subsets of the real number line using brackets and parentheses to indicate whether endpoints are included.

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What does the notation [a, b) mean?

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It means the interval includes 'a' but does not include 'b'.

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

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The 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 slope from two points (x1, y1) and (x2, y2)?

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The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).