Writing System of Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean to solve a system of linear equations?

Back

To solve a system of linear equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

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

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

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 represent the same situation.

Front

What is the meaning of the variables in the equation c + a = 146?

Back

In this equation, c represents the number of children’s tickets sold, and a represents the number of adult tickets sold.

Front

What does the equation 5c + 8a = 1036 represent?

Back

This equation represents the total revenue from ticket sales, where 5 is the price of a children's ticket and 8 is the price of an adult ticket.

Front

What is the perimeter formula for a rectangle?

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 express the relationship between length and width in the problem about the rectangle?

Back

The length L is expressed as L = 3w + 2, meaning the length is two inches more than three times the width.

Front

What is the value of a dime in dollars?

Back

A dime is worth $0.10.

Front

How do you convert the total value of coins into an equation?

Back

If n is the number of nickels and d is the number of dimes, the total value can be expressed as 0.05n + 0.10d = 1.35.