Solving systems by graphing and substitution Flashcard

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the substitution method?

Back

A method for solving a system of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

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

Back

It means the system has no solution because the lines never intersect.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the lines intersect on a graph.

Front

How do you isolate a variable in an equation?

Back

By performing operations to get the variable on one side of the equation by itself.

Front

What is the first step in solving the system 3x + 2y = 10 and x - 5y = 18 using substitution?

Back

Isolate x in the second equation: x = 5y + 18.

Front

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

Back

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

Front

What is the solution to the system of equations y = 2x + 5 and 2x + 2y = 4?

Back

(-1, 3).

Front

What is the significance of the point (1, 3) in a system of equations?

Back

It is the solution where both equations are satisfied.