A linear system gives two equations that must hold for the same pair . Graph both lines in Desmos, then click where they cross: the intersection makes both equations true at once. Read the coordinate the question asks for, rather than automatically using the whole point. The gap between the constants isn't necessarily ; the slopes matter too.
Hints
- Hint 1
A system needs both equations to be true for the same . Each equation describes a line. What point belongs to both lines?
- Hint 2
The intersection is the point shared by the two lines. After you click it, read the pair in order: the first coordinate is , and the second is .
Step-by-step
Approach 1: Graph and read the intersection
Step 1Find the shared point
Type and on separate Desmos lines. Desmos graphs both, and you can see where they cross. A solution must be on both lines, so that crossing is the point you need.
- Step 2
Read the requested coordinate
Click the intersection. Desmos labels the point . In the ordered pair , the first coordinate is , so . The is , which the question doesn't ask for. Choice A.
Approach 2: Set the two expressions for y equal
Step 1Make one equation in x
Both equations give the value of at the same . So at the solution, their right sides must be equal:
This eliminates without finding its value.
- Step 2
Solve for x in Desmos
Type . Here tells Desmos to find an unknown value, and tells it to make the two sides match rather than graph them. Under PARAMETERS, Desmos shows . That's the requested -value. Choice A.