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
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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: \(y = 7\)
