Question 659·Hard·Algebra

Type both equations into Desmos as written, then click their intersection, the point that satisfies both. Desmos shows approximately $(14.429,-3.571)$. The second coordinate is $y$, so you know it's negative. The graph label is rounded; use the equations for an exact answer.

Add the equations. The opposite terms $-2(x-y)$ and $+2(x-y)$ cancel:

Divide both sides by $2$ to find the value of the entire expression $4x+3y$:

Now subtract the whole first equation from the second. The two $4x+3y$ terms cancel. Subtracting the first equation also reverses its $-2(x-y)$, so the remaining pieces add:

Subtract $4(x-y)=72$ from $4x+3y=47$. This cancels the $x$-terms; the minus sign before $4(x-y)$ changes its $-4y$ to $+4y$: $\begin{aligned}(4x+3y)-4(x-y)&=47-72\\4x+3y-4x+4y&=-25\\7y&=-25.\end{aligned}$ Combine equations to get the requested quantity without solving for every variable.

The target $28y$ is four times $7y$. Multiply both sides by $4$: $\begin{aligned}4(7y)&=4(-25)\\28y&=-100.\end{aligned}$ So the value of $28y$ is $-100$. Grid in -100.