Solve the system of equations using elimination: \( x-y=11 \) and \( 5 x+6 y=-44 \). Answer

To solve the system of equations using elimination, we have the following two equations: 1) \( x - y = 11 \) 2) \( 5x + 6y = -44 \) First, we can manipulate equation (1) to express \( x \) in terms of \( y \): \( x = y + 11 \). Now, we can substitute \( x \) into equation (2). Replacing \( x \) gives us: \( 5(y + 11) + 6y = -44 \). Distributing \( 5 \): \( 5y + 55 + 6y = -44 \). Combining like terms: \( 11y + 55 = -44 \). Next, subtract \( 55 \) from both sides: \( 11y = -44 - 55 \) \( 11y = -99 \). Dividing by \( 11 \): \( y = -9 \). Now that we have \( y \), we can substitute it back to find \( x \): Using \( x = y + 11 \): \( x = -9 + 11 \) \( x = 2 \). So the solution to the system of equations is: \( x = 2 \) and \( y = -9 \). Thus, the solution is \( (2, -9) \).