Solving Systems

Front

What is the solution to a system of equations?

Back

The solution is any ordered pair that makes both equations true.

Front

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

Back

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

Front

What does it mean if a system of equations has one solution?

Back

It means the lines intersect at exactly one point.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the lines coincide, or are the same line.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of the line y = 2x + 3?

Back

The y-intercept is 3.

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

Rearrange the equation to solve for y in terms of x.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the intersection of lines on a coordinate plane.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other.