Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

Front

What does it mean for a system of equations to have a solution?

Back

A solution of a system is an ordered pair that satisfies all equations in the system.

Front

What type of lines represent a system of equations with no solution?

Back

Parallel lines represent a system of equations with no solution.

Front

What is the elimination method in solving systems of equations?

Back

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

Front

Solve for x and y: y = 2x + 1, y = 4x - 1

Back

(1, 3)

Front

Solve for x and y: y = 3x - 8, y = 4 - x

Back

(3, 1)

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines on a coordinate plane.

Front

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

Back

If two lines are overlapping, the system has infinitely many solutions.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the difference between intersecting lines and parallel lines in a system of equations?

Back

Intersecting lines have one solution (the point of intersection), while parallel lines have no solutions.