Solve Linear System F947E7

1. **State the problem:** We are given the system of linear equations: $$8x - 3y = -3$$ $$5x - 2y = -1$$ We want to solve this system for $x$ and $y$. 2. **Method:** We will use the elimination method to solve the system. 3. **Elimination step:** Multiply the first equation by 2 and the second equation by 3 to align the coefficients of $y$: $$2(8x - 3y) = 2(-3) \Rightarrow 16x - 6y = -6$$ $$3(5x - 2y) = 3(-1) \Rightarrow 15x - 6y = -3$$ 4. **Subtract the second new equation from the first:** $$ (16x - 6y) - (15x - 6y) = -6 - (-3) $$ $$ 16x - 6y - 15x + 6y = -6 + 3 $$ $$ (16x - 15x) + (-6y + 6y) = -3 $$ $$ x + 0 = -3 $$ $$ x = -3 $$ 5. **Substitute $x = -3$ into one of the original equations, for example the first:** $$8(-3) - 3y = -3$$ $$-24 - 3y = -3$$ 6. **Solve for $y$:** $$-3y = -3 + 24$$ $$-3y = 21$$ $$ y = \frac{21}{-3} $$ $$ y = -7 $$ 7. **Final answer:** $$x = -3, \quad y = -7$$ This is the solution to the system of equations.