systems practice w/applications

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 represent a word problem as a system of equations?

Back

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

Front

What does it mean for a system of equations to have a unique solution?

Back

A unique solution means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

What is the graphical method for solving a system of equations?

Back

The graphical method involves plotting each equation on a graph and identifying the point(s) where they intersect.

Front

What is an infinite number of solutions in a system of equations?

Back

An infinite number of solutions occurs when the equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

No solution means the equations represent parallel lines that never intersect.

Front

How do you check if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation. If all equations are satisfied, the point is a solution.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method for 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.

Front

Define 'dependent' and 'independent' systems of equations.

Back

Dependent systems have infinitely many solutions (the same line), while independent systems have exactly one solution (intersecting lines).