SAT Systems Review :)

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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 to the system is the set of values that satisfy all equations simultaneously.

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How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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What does it mean if two equations represent the same line when graphed?

Back

It means that the system has infinite solutions, as every point on the line is a solution to both equations.

Front

What is the graphical interpretation of a system of equations with no solution?

Back

The lines representing the equations are parallel and never intersect, indicating that there are no values that satisfy both equations.

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How do you solve a system of equations algebraically?

Back

You can use methods such as substitution, elimination, or matrix operations to find the values of the variables that satisfy all equations.

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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 remaining variable.

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What does it mean for two numbers to have a sum of -10 and a difference of -2?

Back

This can be represented by the equations: x + y = -10 and x - y = -2, where x and y are the two numbers.

Front

How can you represent the cost of items in a system of equations?

Back

You can create equations based on the quantities purchased and their total costs, allowing you to solve for the individual prices.

Front

What is the significance of coefficients in a system of equations?

Back

Coefficients represent the relationship between the variables in the equations, indicating how much one variable affects the other.