Solving Systems of Equations by Substitution

Front

What is a system of equations?

Back

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

Front

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

Back

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

Front

What does it mean when a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

How do you solve the system of equations: 2x + 3y = 6 and y = 2x - 1?

Back

Substitute y in the first equation: 2x + 3(2x - 1) = 6, solve for x, then find y.

Front

What is the first step in solving a system of equations by substitution?

Back

Isolate one variable in one of the equations.

Front

If you have the equations y = 3x + 2 and 2x - y = 4, how do you solve them?

Back

Substitute y from the first equation into the second: 2x - (3x + 2) = 4.

Front

What is the solution to the system of equations: 3x - 2y = 7 and y = 2x - 7?

Back

(7, 7) is the solution.

Front

What does it mean if two equations in a system are equivalent?

Back

They represent the same line and will have infinite solutions.

Front

What is the graphical representation of a system of equations?

Back

The points where the lines intersect represent the solutions to the system.