Question Find the solution of the system of equations. \[ \begin{array}{l}2 x+3 y=-2 \\ 4 x+9 y=14\end{array} \] Answer Attempt 1 out of 2

To solve the system of equations, we can use the substitution or elimination method. Let's use elimination here. First, we can multiply the first equation by 2 to align the coefficients of \(x\): \[ 4x + 6y = -4 \] Now, we have the equations: \[ \begin{aligned} 1) & \quad 4x + 6y = -4 \\ 2) & \quad 4x + 9y = 14 \end{aligned} \] Next, subtract the first equation from the second: \[ (4x + 9y) - (4x + 6y) = 14 - (-4) \\ 3y = 18 \\ y = 6 \] Now, substitute \(y = 6\) back into the original first equation: \[ 2x + 3(6) = -2 \\ 2x + 18 = -2 \\ 2x = -20 \\ x = -10 \] Thus, the solution for the system is \((x, y) = (-10, 6)\). When dealing with systems of equations, it's crucial to check your solutions by inserting the values into both original equations. This ensures that the solution satisfies all conditions. Common mistakes arise from careless calculation errors or overlooking signs. Always double-check your arithmetic!