Solving Systems with 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 to solve a system of equations?

Back

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

Front

What is substitution in the context of solving equations?

Back

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

Front

How do you solve for y in the equation y = 2x + 1?

Back

You can find y by substituting a value for x.

Front

What is the first step in solving the system x = 6 and y = 2x - 3?

Back

Substitute x = 6 into the second equation to find y.

Front

What is the solution to the system x = 6 and y = 2x - 3?

Back

(6, 9)

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the graphs of the equations: one intersection means one solution, no intersection means no solution, and overlapping lines mean infinite solutions.

Front

What is the solution to the system 5x - 2y = 3 and y = 2x?

Back

(3, 6)