Module 6 Review 12/12/2024

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 express them in standard form.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable, then substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines or curves on a coordinate plane, where intersections represent solutions.

Front

What is the cost equation for a shoe manufacturer making sandals and running shoes?

Back

Let x = number of sandals, y = number of running shoes. The cost equation is 2.5x + 4y = total cost.

Front

If the shoes cost $6 more than the jacket, how can this be expressed in an equation?

Back

Let x = cost of shoes, y = cost of jacket. The equation is x = y + 6.

Front

What is the first step in solving the system of equations 9x + 11y = -42 and 3x + 4y = -18?

Back

You can use either substitution or elimination to start solving the system.