(2) Unit 6: Systems of Equations - Writing Equations & Solving

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.

Front

How do you write an equation from a word problem?

Back

Identify the variables, translate the relationships and quantities into mathematical expressions, and set them equal to each other based on the problem's context.

Front

What does 'x' typically represent in a system of equations?

Back

In a system of equations, 'x' usually represents one of the unknown quantities we are trying to solve for.

Front

What does 'y' typically represent in a system of equations?

Back

In a system of equations, 'y' usually represents the other unknown quantity we are trying to solve for.

Front

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

Back

Substitute the values of the variables back into the original equations to see if they satisfy both equations.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines representing each equation on a coordinate plane.

Front

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.

Front

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

Back

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

Front

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

Back

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