2x − 3y = −19

4x + 5y = 17

To solve the given system of linear equations, follow these steps:

Step 1: Multiply the first equation by 2 so that the coefficients of x match in both equations:
4x - 6y = -38 (newly multiplied first equation)
4x + 5y = 17 (second equation)

Step 2: Subtract the first equation from the second equation to eliminate the x variable:
(4x + 5y) - (4x - 6y) = 17 - (-38)
11y = 55

Step 3: Divide both sides of the equation by 11 to solve for y:
y = 5

Step 4: Substitute y = 5 back into either of the original equations, e.g., the first equation:
2x - 3(5) = -19
2x - 15 = -19

Step 5: Solve for x:
2x = -4
x = -2

Therefore, the solution to the given system of equations is x = -2 and y = 5, or (-2, 5).