4.10-4.11 Solutions to Systems

Front

What is a solution to a system of equations?

Back

A solution is an ordered pair (x, y) that satisfies all equations in the system.

Front

How do 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 both equations are true, the point is a solution.

Front

What does it mean if two lines intersect on a graph?

Back

The intersection point represents the solution to the system of equations, where both equations are satisfied.

Front

What is the graphical representation of a system of equations?

Back

It is represented by two or more lines on a coordinate plane.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point on a coordinate plane.

Front

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

Back

If two lines are parallel, they have no points in common, meaning there is no solution to the system.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x=0.

Front

How can you find the y-intercept from a linear equation in slope-intercept form?

Back

In the equation y = mx + b, b is the y-intercept.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run (change in y over change in x).

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 every point on the line is a solution.