“Systems” Explained – Inlighten Tutoring

"System of Equations" Explained

Plug into DESMOS, then look for intersection.

Key Idea: System of Equations

A system of equations is a set of two or more equations with the same variables.
The solution is the point(s) where the equations are simultaneously true.

General Rule:

Solve by substitution, elimination, or graphing.
Graphically, the solution is the intersection point(s) of the equations’ graphs.
Can have one solution, infinitely many solutions, or no solution.

Why this matters for the SAT:

System of equations problems test your ability to combine algebra and graphing.
Tools like Desmos can help visualize intersections quickly for checking solutions.

"Systems of Inequalities" Explained

Solutions lie in overlapping shaded regions.

Key Idea: Systems of Inequalities

A system of inequalities consists of two or more inequalities with the same variables.
The solution is the set of points that satisfy all inequalities at once.

General Rule:

Graph each inequality on a coordinate plane.
The solution is the overlapping (shaded) region of all inequalities.
Some systems may have no solution if regions don’t overlap.

Why this matters for the SAT:

Systems of inequalities appear in coordinate geometry and word problems.
Recognizing the overlapping region helps you quickly identify all solutions that satisfy the system.

"Intersects" Explained

Where one function meets another.

Key Idea: Intersects

Intersects refers to the point(s) where two graphs or functions meet.

General Rule:

The x-coordinate of an intersection satisfies both equations simultaneously.
The y-coordinate is the common output at that x-value.

Why this matters for the SAT:

Finding intersections is key for solving systems of equations, analyzing graphs, and interpreting function behavior. It tells you where two relationships occur at the same time.