2 solve the system by substitution \( y=4 x-7 \) \( 7 x+4 y=-5 \)

To solve the system, we start by substituting the expression for \( y \) from the first equation into the second equation. So we replace \( y \) in \( 7x + 4y = -5 \) with \( 4x - 7 \): \[ 7x + 4(4x - 7) = -5 \] This simplifies to: \[ 7x + 16x - 28 = -5 \] Combine like terms: \[ 23x - 28 = -5 \] Now, add 28 to both sides: \[ 23x = 23 \] Dividing each side by 23 gives: \[ x = 1 \] Now substitute \( x = 1 \) back into the first equation to find \( y \): \[ y = 4(1) - 7 = 4 - 7 = -3 \] Thus, the solution to the system is \( (1, -3) \). So, your solutions are \( x = 1 \) and \( y = -3 \). Feel free to double-check by plugging these values back into the second equation to confirm they satisfy both equations!