A system of equations gives two conditions that must hold for the same pair . Graph both equations in Desmos and click their intersection, the point on both lines. The first coordinate is and the second is , so check which coordinate the question asks for before choosing an answer.
Hints
- Hint 1
A system requires the same pair to make both equations true. Each equation draws a line in Desmos. Where could you find a point that lies on both lines?
- Hint 2
An intersection is where the lines cross. Desmos shows that point as , with first. Which coordinate does the question ask you to report?
Step-by-step
Approach 1: Read the intersection in Desmos
Step 1Graph the first equation
Type on the first line in Desmos. It draws a line of points that satisfy this equation alone. A point must satisfy the second equation too to solve the system.
- Step 2
Read the requested coordinate
Add on the next line and click the intersection. Desmos shows . That point satisfies both equations. In , comes first, so read the coordinate the question asks for: . Choice C.
Approach 2: Cancel the y-terms by hand
Step 1Add the equations to remove y
This is elimination: and are opposites, so adding the equations cancels them. Add both sides:
Combine terms:
- Step 2
Solve for x
Divide both sides by :
Simplify:
You have the requested value of , so there's no need to find . Choice C.