Writing Systems of Equations from Word Problems

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 in the system.

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 ensure the equations reflect the problem's constraints.

Front

In the equation 6t + 8g = 50, what do t and g represent?

Back

In this equation, t represents the price of a tigerfish and g represents the price of a goldfish.

Front

What does the equation x + y = 6 represent in a word problem?

Back

This equation typically represents a scenario where x and y are quantities that add up to 6, such as the number of items sold.

Front

What is the significance of coefficients in a system of equations?

Back

Coefficients represent the number of units of each variable in the context of the problem, indicating how they contribute to the total.

Front

How do you determine the total cost in a word problem involving prices?

Back

Multiply the quantity of each item by its price and sum the results to find the total cost.

Front

What is the perimeter of a rectangle formula?

Back

The perimeter P of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.

Front

How do you solve a system of equations graphically?

Back

Graph each equation on the same coordinate plane. The point where the lines intersect represents the solution to the system.

Front

What does it mean if two equations in a system are parallel?

Back

If two equations are parallel, they have no points of intersection, meaning there is no solution to the system.

Front

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

Back

The first step is to define the variables that represent the unknown quantities in the problem.