Question Solve the system by substitution. \[ \begin{array}{r}-10 y=x \\ -5 x-7 y=43\end{array} \] Answer Attempt 1 out of 2

To solve the system using substitution, let's first express \( x \) in terms of \( y \) using the first equation: \[ x = -10y. \] Now, substitute \( x \) into the second equation: \[-5(-10y) - 7y = 43.\] This simplifies to: \[50y - 7y = 43,\] which combines to: \[43y = 43.\] Thus, \( y = 1 \). Now substitute \( y = 1 \) back into the equation \( x = -10y \) to find \( x \): \[ x = -10(1) = -10.\] So the solution to the system is \( (x, y) = (-10, 1) \). Now, let’s ensure we check our work! Always plug your solution back into the original equations to validate: For the first equation: \[-10(1) = -10\] (✓) And for the second equation: \[-5(-10) - 7(1) = 50 - 7 = 43\] (✓) Both equations are satisfied, so our solution is confirmed!