Solve the system of equations by any method. \[ -2 x+5 y=-21 \] \[ 7 x+2 y=15 \] Enter the exact answer as an ordered pair, \( (x, y) \). If there is no solution, enter NS. If there is an infinite number of solutions, enter the general solution as an ordered pair in terms of \( x \). Include a multiplication sign between symbols. For example, \( a^{*} x \). I \[ \text {. } \] \[ \text {. } \]

To solve the system of equations 1. \(-2x + 5y = -21\) 2. \(7x + 2y = 15\), we can use the method of substitution or elimination. Here, let's use elimination. First, we can multiply the first equation by 7 and the second equation by 2 to align the coefficients of \(x\): \[ 7(-2x + 5y) = 7(-21) \implies -14x + 35y = -147 \] \[ 2(7x + 2y) = 2(15) \implies 14x + 4y = 30 \] Next, we add these two equations: \[ (-14x + 35y) + (14x + 4y) = -147 + 30 \] This simplifies to: \[ 39y = -117 \] Dividing by 39 gives us: \[ y = -3 \] Now, substitute \(y = -3\) back into one of the original equations to find \(x\). We'll use the first equation: \[ -2x + 5(-3) = -21 \] This simplifies to: \[ -2x - 15 = -21 \] Add 15 to both sides: \[ -2x = -6 \] Finally, divide by -2: \[ x = 3 \] Thus, the solution to the system of equations is \((3, -3)\).