$\left\{\begin{array} { l } 12x+15y=-1.5 \\ 3x+7y=0.6\end{array} \right.$
Multiply both sides of the equation by $-4$$\left\{\begin{array} { l } 12x+15y=-1.5 \\ -12x-28y=-2.4\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$-13y=-3.9$
Divide both sides of the equation by $-13$$y=0.3$
Substitute the given value of $y$ into the equation $4x+5y=-0.5$$4x+5 \times 0.3=-0.5$
Solve the equation for $x$$x=-\frac{ 1 }{ 2 }$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( -\frac{ 1 }{ 2 }, 0.3\right)$
Convert the decimal into a fraction$\left( x, y\right)=\left( -\frac{ 1 }{ 2 }, \frac{ 3 }{ 10 }\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 4 \times \left( -\frac{ 1 }{ 2 } \right)+5 \times \frac{ 3 }{ 10 }=-0.5 \\ 3 \times \left( -\frac{ 1 }{ 2 } \right)+7 \times \frac{ 3 }{ 10 }=0.6\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } -\frac{ 1 }{ 2 }=-\frac{ 1 }{ 2 } \\ \frac{ 3 }{ 5 }=\frac{ 3 }{ 5 }\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( -\frac{ 1 }{ 2 }, \frac{ 3 }{ 10 }\right)$