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 to solve a system of equations by substitution?

Back

It means to solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the graphical representation of a system of equations?

Back

The solution is the point where the graphs of the equations intersect.

Front

What does it indicate if two equations represent parallel lines?

Back

The system has no solution because the lines never intersect.

Front

What does it indicate if two equations represent the same line?

Back

The system has infinite solutions because every point on the line is a solution.

Front

How do you determine if a system of equations has a unique solution?

Back

If the lines intersect at exactly one point, the system has a unique solution.

Front

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

Back

Solve one of the equations for one variable.

Front

Given the equations y = 2x + 1 and y = 4x - 1, what is the solution?

Back

(1, 3)

Front

What is the solution to the system of equations 3x + 2y = 8 and -x + y = -11?

Back

(6, -5)

Front

What does the equation 4 = 7 represent in terms of solutions?

Back

It represents a contradiction, indicating no solution.