Illustrative Math Algebra Unit 2

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 if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations. If they are parallel, there is no solution; if they are the same line, there are infinitely many solutions; if they intersect at one point, there is one solution.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the revenue function for a business?

Back

Revenue is calculated by multiplying the price per item by the number of items sold, represented as R = p * x, where p is price and x is quantity.

Front

What is the expense function for a business with fixed and variable costs?

Back

Expense is calculated as the sum of fixed costs and variable costs, represented as E = F + V*x, where F is fixed costs, V is variable cost per item, and x is quantity.

Front

What is the solution to the equation 5x - 4 + 2x = 3?

Back

x = 1.

Front

What does it mean for a solution to be (1, -1) in a system of equations?

Back

It means that when x = 1, y = -1 satisfies both equations in the system.

Front

How do you graph a system of equations?

Back

By plotting each equation on the same coordinate plane and identifying points of intersection.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where both equations are satisfied.