Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for two lines to intersect on a graph?

Back

It means they have a common solution (x, y) that satisfies both equations.

Front

What is the solution to a system of equations?

Back

The point (x, y) where the equations intersect.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect.

Front

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

Back

The equations represent the same line, so every point on the line is a solution.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the slope of a line?

Back

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

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

Use the formula: slope = (y2 - y1) / (x2 - x1).

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane.

Front

What does it mean if two lines are perpendicular?

Back

Their slopes are negative reciprocals of each other.