A system of linear equations gives two rules for the same . Graph both equations as written in Desmos and click their intersection: both equations hold at the crossing point. Read the coordinate the question asks for, rather than taking a number from only one line. When the -terms are opposites, adding the equations is a fast hand route.
Hints
- Hint 1
An intersection is where two graphed lines meet. Desmos can graph these equations as written, without rearranging either one. Which point lies on both lines?
- Hint 2
In an ordered pair , is the first coordinate. After you click the crossing point, which displayed number answers the question?
Step-by-step
Approach 1: Graph the system in Desmos
Step 1Graph both equations
Type and on separate Desmos lines. Their graphs cross once. That intersection lies on both lines, so its coordinates satisfy both equations.
- Step 2
Read the requested coordinate
Click the crossing point. Desmos shows approximately . In , is the first coordinate, so the value of is , not the second number. Choice C.
Approach 2: Cancel the opposite terms by hand
Step 1Add the equations to remove y
The -terms are and , so they add to zero. This is elimination: adding equal amounts on each side of two equations keeps the sides equal. Add both entire equations:
- Step 2
Combine the remaining terms
The -terms cancel, leaving only . Combine the terms on each side:
- Step 3
Solve for x
Divide both sides by : . That's the value of the question asks for. Choice C.