AIA Ch 5 Systems of Equations & Inequalities

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a solution to a system of equations to be consistent?

Back

A consistent system has at least one solution.

Front

What does it mean for a solution to a system of equations to be inconsistent?

Back

An inconsistent system has no solutions.

Front

What is the graphical representation of a linear inequality?

Back

A region of the coordinate plane that satisfies the inequality, often represented with a dashed or solid line.

Front

How do you solve a linear inequality?

Back

Isolate the variable on one side of the inequality sign, similar to solving an equation.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than, while '≥' means greater than or equal to.

Front

What is the solution to the inequality 11x + 16 < 43 + 2x?

Back

x < 3.

Front

What does the graph of x < -1 look like?

Back

A dashed vertical line at x = -1, shading to the left.

Front

What is a system of equations used to represent in real-life problems?

Back

It can represent relationships between quantities, such as money and items.

Front

How do you write a system of equations for the problem: Dennis mowed his neighbor’s lawn for dimes and nickels, totaling 80 coins and $6.60?

Back

d + n = 80 and 0.10d + 0.05n = 6.60.