Solve Systems by Inspection

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 by inspection?

Back

To find the solution by looking at the equations and identifying points that satisfy both equations without formal calculations.

Front

What are the possible types of solutions for a system of equations?

Back

One Solution, No Solution, Infinitely Many Solutions.

Front

What is the meaning of 'One Solution'?

Back

There is exactly one set of values for the variables that satisfies all equations in the system.

Front

What does 'No Solution' indicate in a system of equations?

Back

The equations represent parallel lines that never intersect.

Front

What does 'Infinitely Many Solutions' mean?

Back

The equations represent the same line, meaning any point on the line is a solution.

Front

How can you determine if a system has no solution?

Back

If the equations are parallel and have different y-intercepts.

Front

What is the solution to the system: y = 2x + 3 and y = 2x - 1?

Back

No Solution.

Front

What is the solution to the system: y = x + 2 and y = -x + 2?

Back

(0, 2).

Front

How do you find the solution to the system: y = 3x + 1 and y = -3x + 7?

Back

Set the equations equal to each other: 3x + 1 = -3x + 7, solve for x, then substitute back to find y.