7 Solve the given linear system of equations: \( 5 x+3 y=-9 \) \( -10 x-9 y=-3 \) \( y=\square \) Question Help: \( \square \) Message instructor

To solve the system of equations, we can use the method of substitution or elimination. Let's use elimination for this example. First, we can manipulate the first equation \(5x + 3y = -9\) by multiplying it by 2, to align it with the second equation which has coefficients suitable for elimination: \[ 2(5x + 3y) = 2(-9) \implies 10x + 6y = -18 \] Now we have: 1. \(10x + 6y = -18\) 2. \(-10x - 9y = -3\) Next, we can add both equations: \[ (10x - 10x) + (6y - 9y) = -18 - 3 \] This simplifies to: \[ -3y = -21 \] Thus, solving for \(y\): \[ y = 7 \] Now, substitute \(y = 7\) back into the first equation to solve for \(x\): \[ 5x + 3(7) = -9 \] \[ 5x + 21 = -9 \] \[ 5x = -30 \implies x = -6 \] So, the solution to the system of equations is \(x = -6\) and \(y = 7\). The final answer is: \(y = 7\)