Find the solution of the system of equations: 8x - 2y = -30; -9x + 4y = 18.

Steps to Solve

1. Rewrite the equations in a standard form

   The equations are already in standard form. Here they are: $$ 8x - 2y = -30 $$ $$ -9x + 4y = 18 $$

2. Multiply the first equation by 2

   To eliminate $y$, we can multiply the first equation by 2: $$ 2(8x - 2y) = 2(-30) $$

   This simplifies to: $$ 16x - 4y = -60 $$

3. Align the equations for elimination

   Now we have the transformed first equation: $$ 16x - 4y = -60 $$ and the second equation: $$ -9x + 4y = 18 $$

4. Add the two equations

   Now, we can add these two equations to eliminate $y$: $$ (16x - 4y) + (-9x + 4y) = -60 + 18 $$

   This simplifies to: $$ 7x = -42 $$

5. Solve for $x$

   Divide both sides by 7: $$ x = -6 $$

6. Substitute $x$ back into one of the original equations

   We'll substitute $x = -6$ into the first equation: $$ 8(-6) - 2y = -30 $$ This simplifies to: $$ -48 - 2y = -30 $$

7. Solve for $y$

   Rearranging gives: $$ -2y = -30 + 48 $$ $$ -2y = 18 $$ Divide by -2: $$ y = -9 $$

8. Final Solution

   Thus, the solution to the system of equations is: $$ (x, y) = (-6, -9) $$