UNIT 6 System of Equations Flashcard #2

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 if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you solve a system of equations by graphing?

Back

You graph each equation on the same coordinate plane and identify the point(s) where they intersect.

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.

Front

What is the graphical representation of the equation y = 2x - 11?

Back

A straight line with a slope of 2 and a y-intercept of -11.

Front

What is the slope of the line represented by the equation -4x - 2y = -12?

Back

The slope is 2, found by rearranging the equation into slope-intercept form (y = mx + b).

Front

What does the term 'solution' refer to in the context of a system of equations?

Back

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

Front

What is the significance of the point (3, 3) in a system of equations?

Back

It is the point where the two lines intersect, representing the solution to the system.