Writing Systems of Equations and Inequalities

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 set of values that satisfy all equations simultaneously.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of values that satisfy all inequalities simultaneously.

Front

How do you represent a situation with a system of inequalities?

Back

Identify the constraints and objectives, then express them as inequalities using variables to represent quantities.

Front

What does the symbol '≤' mean in inequalities?

Back

'≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean in inequalities?

Back

'≥' means 'greater than or equal to', indicating that the value on the left can be greater than or equal to the value on the right.

Front

How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane, shading the region that satisfies each inequality. The solution is where the shaded regions overlap.

Front

What is the first step in solving a system of equations?

Back

The first step is to express one variable in terms of the other using one of the equations.

Front

What is the substitution method in 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 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.

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, which means they never intersect.