Question

Find all solutions for the following systems with complex coefficients. (If there are an infinite number of solutions, use(5−5i)x1+ 50 x2

Answer 1

To solve a system of equations with complex coefficients, you can use the methods of substitution or elimination. These methods involve simplifying and solving the equations to find the values of the variables.

Step-by-step explanation:

To solve the system of equations with complex coefficients, we can use the method of substitution or elimination. Let's consider an example:

Example:

2x + 3y = 7

x - 2y = 5 + 2i

We can solve this system using substitution:

1. From the second equation, solve for x: x = 5 + 2i + 2y
2. Substitute this value of x into the first equation: 2(5 + 2i + 2y) + 3y = 7
3. Simplify and solve for y
4. Substitute the value of y back into the second equation to find x

Alternatively, you can also solve this system using elimination:

1. Multiply the second equation by 2 to make the coefficients of x in both equations equal
2. Subtract the second equation from the first equation to eliminate x
3. Solve for y
4. Substitute the value of y back into either equation to find x