1. **State the problem:** Solve the system of linear equations: $$4x + 3y = 15$$ $$6x - 2y = -10$$ 2. **Formula and rules:** We can solve this system using the elimination or substitution method. Here, we'll use elimination to eliminate one variable. 3. **Multiply equations to align coefficients:** Multiply the first equation by 2 and the second by 3 to align the coefficients of $y$: $$2(4x + 3y) = 2(15) \Rightarrow 8x + 6y = 30$$ $$3(6x - 2y) = 3(-10) \Rightarrow 18x - 6y = -30$$ 4. **Add the two equations to eliminate $y$:** $$8x + 6y + 18x - 6y = 30 + (-30)$$ $$ (8x + 18x) + (6y - 6y) = 0$$ $$26x + \cancel{0} = 0$$ 5. **Solve for $x$:** $$26x = 0$$ $$x = \frac{0}{26} = 0$$ 6. **Substitute $x=0$ into one original equation to find $y$:** Using the first equation: $$4(0) + 3y = 15$$ $$0 + 3y = 15$$ $$3y = 15$$ $$y = \frac{15}{3} = 5$$ 7. **Final solution:** $$\boxed{(x, y) = (0, 5)}$$ This means the two lines intersect at the point $(0,5)$.