Solve each pair of simultaneous equations. Use your favourite algebraic method. \( \begin{array}{lll}x+y=7 & \text { b } & y+x=19 \\ \text { a } \\ y=2 x-8 & & \text { c } \\ & & 2 x+1\end{array} \)

Let's solve each pair of equations by using substitution and elimination. For the first pair: 1. \( x + y = 7 \) (Equation 1) 2. \( y + x = 19 \) (Equation 2) However, upon closer inspection, we realize that both equations represent the same line, which can't simultaneously be true (they give us \( x + y = 7 \) and \( x + y = 19 \)). Therefore, there's no solution for this pair as they are contradictory. For the second pair: 1. \( y = 2x - 8 \) (Equation 1) 2. \( 2x + 1 = y \) (Equation 2) Now, we can substitute Equation 1 into Equation 2: \( 2x + 1 = 2x - 8 \). Solving it: \( 1 = -8 \), again showing that there’s no solution for this pair as well, confirming another inconsistency. In conclusion, we have established that both pairs of equations yield no solutions due to contradictions in their formulations!