Systems Substitution

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 that the equations represent parallel lines that never intersect.

Front

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

Back

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

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the graphical representation of a system of equations?

Back

The solutions are represented by the points where the graphs of the equations intersect.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

What is the solution to the system of equations: 2x + 3y = 6 and 4x + 6y = 12?

Back

Infinite solutions.

Front

What is the solution to the system of equations: x + y = 5 and x - y = 1?

Back

(3, 2)

Front

What is the substitution method?

Back

A method for solving systems of equations by expressing one variable in terms of another and substituting it into the other equation.

Front

What does it mean for two lines to be coincident?

Back

It means they lie on top of each other, representing infinite solutions.