The graph of a system of two linear equations is shown. Which choice gives the solution to the system?
A system is two equations using the same variables. On a graph, the point where the lines cross solves both equations because it lies on both lines. Read the horizontal coordinate before the vertical coordinate to form . Reversing that order is a common trap; if the crossing is already marked, you don't need Desmos.
Hints
- Hint 1
The intersection is the point where two lines cross. It lies on both lines, so its coordinates solve both equations. Which marked point is shared by the lines?
- Hint 2
An ordered pair lists the horizontal -coordinate first and the vertical -coordinate second. From the shared point, follow the grid to each axis to read those coordinates.
Step-by-step
Read the marked intersection
Step 1Find the point that solves both equations
No Desmos needed. The crossing is already marked on the graph. The solid dot is where the lines cross. That intersection sits on both lines, so it solves both equations.
- Step 2
Read the horizontal coordinate
Follow the grid straight down from the dot to the -axis. Its horizontal position is , so .
- Step 3
Read the vertical coordinate
Follow the grid left from the dot to the -axis. Its vertical position is , so . Put first and second: the solution is . Choice A.