Question 279·Medium·Algebra

Type $2x+y=10$ and $3x-y=5$ on separate Desmos lines as written. Desmos draws two lines that cross. Their intersection lies on both lines, so its coordinates satisfy both equations. Typing $3x-y=5$ directly also avoids a sign slip from rearranging it.

Click the intersection. Desmos labels it $(3,4)$. An ordered pair $(x,y)$ lists $x$ first and $y$ second, so the second coordinate gives the requested $y=4$, not $x=3$. Grid in 4.

The equations have $+y$ and $-y$. In elimination, you add matching sides of the equations so those terms cancel. Add the whole equations:

Combine the terms:

Divide both sides by $5$: $x=3$. This is the first coordinate, not the $y$ the question asks for.

Replace $x$ with $3$ in the first equation, $2x+y=10$:

Multiply $2$ and $3$: $6+y=10$. The $6$ is only the $x$-term; there's still a $y$ to find.

Subtract $6$ from both sides: $y=4$. The requested value of $y$ is $4$. Grid in 4.