Flashcard - Solve 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 if a system of equations has no solution?

Back

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

Front

What is the graphical representation of a system of equations?

Back

The solution is represented by the point(s) where the graphs of the equations intersect.

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) of intersection.

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 infinitely many solutions?

Back

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

Front

What is the substitution method for 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 for solving systems of equations?

Back

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

Front

Solve the system: 3x - 2y = 7 and y = 2x - 7.

Back

(7, 7)

Front

Solve by graphing: y = 2x + 1 and y = 4x - 1.

Back

(1, 3)