To determine if \((10, 8)\) is a solution to the system of equations given:
- \(13x + 4y = -2\)
- \(12x - 14y = 8\)
we need to substitute \(x = 10\) and \(y = 8\) into both equations and see if the equations hold true.
First equation: \[ 13(10) + 4(8) = -2 \] Calculating the left side: \[ 130 + 32 = 162 \] We see that: \[ 162 \neq -2 \] So, \((10, 8)\) does not satisfy the first equation.
Second equation: \[ 12(10) - 14(8) = 8 \] Calculating the left side: \[ 120 - 112 = 8 \] We see that: \[ 8 = 8 \] So, \((10, 8)\) satisfies the second equation.
Since \((10, 8)\) does not satisfy the first equation, we conclude that \((10, 8)\) is not a solution to the system of equations.