Block 2 Systems with Substitutions

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

Replacing one variable with an expression involving another variable.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into each equation; if it satisfies all, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

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

Back

Isolate one variable in one of the equations.

Front

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

Back

(1, 3)

Front

What is the significance of the solution to a system of equations?

Back

It represents the point(s) where the equations intersect, indicating the values of the variables.

Front

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

Back

The lines are parallel and do not intersect.

Front

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

Back

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