Question

what is the solution to the system graphed below?

(1, 1)
(1, -1)
(-1, 1)
(-1, -1)

Explanation:

🆕 New Concept Discovered: Graphical Solution to Systems
Where two lines cross is the shared solution.

Step 1: Identify the intersection point

To find the solution to a system of equations from a graph, we look for the point where the two lines intersect. This intersection point represents the coordinate pair \((x, y)\) that satisfies both equations simultaneously.

Looking at the graph, the two lines cross each other in the lower-left quadrant (Quadrant III).

Step 2: Read the coordinates of the intersection

1. Find the position along the horizontal \(x\)-axis:

Moving left from the origin \((0,0)\) by \(1\) unit gives an \(x\)-coordinate of \(-1\).

1. Find the position along the vertical \(y\)-axis:

Moving down from the origin \((0,0)\) by \(1\) unit gives a \(y\)-coordinate of \(-1\).

The intersection point is \((-1, -1)\).

Answer:

\((-1, -1)\)