Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have no solution?

Back

It means the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The equations represent the same line, meaning they overlap completely.

Front

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

Back

Substitute the point's coordinates into each equation; if both equations are true, the point is a solution.

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

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does it mean if two lines are intersecting?

Back

It means they have one solution, which is the point where they cross.

Front

What is the solution to the system of equations: y = 2x + 3 and y = -x + 1?

Back

(−2, −1) is the solution.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.