Answer :
To solve for \(x\) and \(y\) given the equation \((5y - 2) + i(3x - y) = 3 - 7i\), we need to equate the real and imaginary parts separately. Let's break it down step-by-step:
1. Identify the real and imaginary parts:
[tex]\[ (5y - 2) + i(3x - y) = 3 - 7i \][/tex]
2. Equate the real parts:
[tex]\[ 5y - 2 = 3 \][/tex]
Solve for \(y\):
[tex]\[ 5y - 2 = 3 \\ 5y = 5 \\ y = 1 \][/tex]
3. Equate the imaginary parts:
[tex]\[ 3x - y = -7 \][/tex]
Substitute \(y = 1\):
[tex]\[ 3x - 1 = -7 \\ 3x = -6 \\ x = -2 \][/tex]
Hence, the values of \(x\) and \(y\) that satisfy the equation \((5y - 2) + i(3x - y) = 3 - 7i\) are:
[tex]\[ x = -2 \quad \text{and} \quad y = 1 \][/tex]
1. Identify the real and imaginary parts:
[tex]\[ (5y - 2) + i(3x - y) = 3 - 7i \][/tex]
2. Equate the real parts:
[tex]\[ 5y - 2 = 3 \][/tex]
Solve for \(y\):
[tex]\[ 5y - 2 = 3 \\ 5y = 5 \\ y = 1 \][/tex]
3. Equate the imaginary parts:
[tex]\[ 3x - y = -7 \][/tex]
Substitute \(y = 1\):
[tex]\[ 3x - 1 = -7 \\ 3x = -6 \\ x = -2 \][/tex]
Hence, the values of \(x\) and \(y\) that satisfy the equation \((5y - 2) + i(3x - y) = 3 - 7i\) are:
[tex]\[ x = -2 \quad \text{and} \quad y = 1 \][/tex]
