The solution to the simultaneous equations \[ 5 x+4 y=14 \text { and } 3 x-4 y=2 \]

Step 1 ：Multiply the first equation by 3 and the second equation by 5 to make the coefficients of y equal: \(15x + 12y = 42\) and \(15x - 20y = 10\)

Step 2 ：Subtract the second equation from the first to eliminate y: \(32y = 32\)

Step 3 ：Divide by 32 to find the value of y: \(y = 1\)

Step 4 ：Substitute the value of y back into one of the original equations to find the value of x: \(5x + 4(1) = 14\)

Step 5 ：Solve for x: \(5x = 10\) and \(x = 2\)

Step 6 ：\(\boxed{x = 2}\) and \(\boxed{y = 1}\)