System of linear equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the graphical representation of a system of linear equations?

Back

The lines representing the equations on a graph; the intersection point(s) represent the solution(s).

Front

How do you find the break-even point in a business scenario?

Back

Set total revenue equal to total costs and solve for the quantity of goods sold.

Front

What is the formula for the perimeter of a rectangle?

Back

P = 2(length + width) or P = 2L + 2W.

Front

If the length of a rectangle is 8 inches more than three times the width, how can you express this relationship mathematically?

Back

Length (L) = 3*Width (W) + 8.

Front

What is the cost function in a business context?

Back

A mathematical function that describes the total cost of producing a certain number of goods.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the rate of change of the dependent variable with respect to the independent variable.

Front

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

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

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

Back

A system is consistent if it has at least one solution.