Chapter 5: Simultaneous Linear Equations

Flashcards about linear equations

What is the independent variable?

When a number is substituted for a variable.

What is a dependent variable?

The variable that depends on the number substituted for the independent variable.

What is the gradient-intercept formula?

y = mx + c. where m is the slope or gradient, and c is the y-intercept.

How is the gradient of a line calculated?

By dividing the vertical rise by the horizontal run.

What does it mean if two linear functions have the same m-value?

The lines are parallel.

What is the first step when sketching a linear function using the gradient and y-intercept?

Rearrange the equation into gradient form y = mx + c.

What is linear modeling?

When a practical situation is described mathematically using a linear function.

In a linear model, what does the gradient represent?

The rate per unit or interval.

In a linear model, what does the vertical axis intercept represent?

The initial value or starting point.

What is the key idea behind solving simultaneous equations graphically?

Finding the point of intersection of two straight lines.

What does the point of intersection represent in practical applications of simultaneous equations?

The solution that satisfies both equations, often a break-even point.

What are the two algebraic methods for solving simultaneous equations?

Substitution and elimination.

What is the substitution method for solving simultaneous equations?

Substituting a variable from one equation into the other equation.

What is the elimination method for solving simultaneous equations?

Eliminating one of the unknown variables by adding or subtracting the two equations.

What does the point of intersection represent in simultaneous equation models of practical situations?

A solution that has an important meaning depending on the situation, such as a business changing from a loss to a profit.

What is the break-even point?

The point where costs or expenses and income are equal, resulting in no profit or loss.

How is profit calculated?

Profit = Income – Costs

I = mx represents Income. What does x and m represent?

x = number of items sold; m = selling price of each item

C = mx + c represents Cost. What does x, m, and c represent?

x = number of items sold; m = cost price per item manufactured ; c = fixed costs of production.