Substitution- Algebra 1

Front

What is a system of equations?

Back

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

Front

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

Back

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

Front

How can you determine if a system of equations has no solution?

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

Front

What is the graphical representation of a system of equations with one unique solution?

Back

Two lines that intersect at exactly one point.

Front

What is the solution to the system of equations represented by y = 2x + 3 and y = -x + 1?

Back

(1, 5) - The point where the two lines intersect.

Front

What does the term 'substitution' refer to in algebra?

Back

A method for solving systems of equations by replacing one variable with an expression involving the other variable.

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 solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0) - The point where the two lines intersect.

Front

What is the significance of the point (7, -2) in a system of equations?

Back

It is the unique solution where the two equations intersect.

Front

What does it mean if the solution to a system of equations is (-2, -2)?

Back

It indicates that both equations are satisfied when x = -2 and y = -2.