jmc

We can find $x$ by adding twice the first equation to five times the second. From $$\begin{array}{rl}2(3x-5y)+5(7x+2y)& =6x+35x\\ & =41x,\end{array}$$and $$\begin{array}{rl}2(3x-5y)+5(7x+2y)& =2(-1.5)+5(4.7)\\ & =-3+23.5\\ & =20.5,\end{array}$$we find that $41x=20.5$, or $x=\mathrm{0.5.}$

Substituting into the second equation, we can find $y:$ $$\begin{array}{rl}7x+2y& =4.7\\ ⟹y& =\frac{1}{2}(4.7-7x)\\ & =\frac{1}{2}(4.7-3.5)\\ & =\frac{1}{2}(1.2)\\ & =\mathrm{0.6.}\end{array}$$Thus our answer is $\boxed{(0.5,0.6)}.$