Question 133·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

No Desmos needed. Hand algebra gives a formula that works for every $u$ and $w$. To isolate $v$, leave it alone on one side. The $3u$ is added to $2v$, so subtract $3u$ from both sides: $2v=w-7-3u$.

The coefficient $2$ multiplies $v$. Divide both whole sides by $2$, keeping $w-7-3u$ together: $v=\frac{w-7-3u}{2}$. This expresses $v$ in terms of $u$ and $w$. Choice B.

There are no restrictions on $u$ and $w$, so try $u=2$ and $w=11$. Type those values, then type $3u+2v_1\sim w-7$. The $\sim$ tells Desmos to solve for $v_1$ rather than graph the equation. Under PARAMETERS, it reports $v_1=-1$. Any correct formula must give $-1$ for these inputs.

Type each proposed right side on its own line. Desmos prints $2$, $-1$, $5$, and $1$, in that order. Only the second formula gives the required $-1$, so this sample rules out the other three. A sample alone doesn't prove a formula works for every input; the hand algebra above does. The formula is $v=\frac{w-7-3u}{2}$. Choice B.