NHS: Systems Flashcard 1

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 find the sum of two numbers?

Back

To find the sum of two numbers, simply add them together. For example, if the numbers are x and y, the sum is x + y.

Front

What does it mean for two numbers to have a difference?

Back

The difference between two numbers is the result of subtracting one number from the other. For example, if x and y are two numbers, the difference is x - y.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented as (0, b) where b is the value of y when x = 0.

Front

What is slope in a linear equation?

Back

Slope is a measure of the steepness of a line, calculated as the rise over run. In the equation y = mx + b, m represents the slope.

Front

How do you graph a line using the slope-intercept form?

Back

1. Plot the y-intercept (0, b). 2. Use the slope (rise/run) to find another point. 3. Draw the line through the points.

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all equations true simultaneously.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into each equation. If the point satisfies all equations, it is a solution.

Front

What does it mean for a point to be part of the solution set?

Back

A point is part of the solution set if it satisfies all equations in the system, meaning it makes all equations true.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection of the lines represented by the equations. The intersection point(s) are the solutions.