Solve the system: 2x - 3y = 18 and 5x + 4y = -1.

Answer

To solve this system of linear equations using the elimination method, we will eliminate one variable by making its coefficients opposites. Let's eliminate 'y'. Step 1: Find a common multiple for the coefficients of 'y' (3 and 4), which is 12. Multiply the first equation by 4 and the second equation by 3. This gives: (1) 8x - 12y = 72 and (2) 15x + 12y = -3. Step 2: Add the two equations together to eliminate 'y'. (8x + 15x) + (-12y + 12y) = 72 + (-3), which simplifies to 23x = 69. Step 3: Solve for x. Dividing both sides by 23 gives x = 3. Step 4: Substitute x = 3 into one of the original equations to solve for y. Using the first equation: 2(3) - 3y = 18, so 6 - 3y = 18. Subtract 6 from both sides: -3y = 12. Divide by -3: y = -4. The final solution is the ordered pair (3, -4).