MHB Find x and y if x, y are members of real numbers and: (x+i)(3-iy)=1+13i

[Gladier]

Find x and y if x, y are members of real numbers and: (x+i)(3-iy)=1+13i

I first expanded it to give: 3x-yix+3i+y=1+13i
Then I equaled 3x+y=1 and -yx+3=13
But afterwards I do other steps and get the wrong answer.

 

[Greg]

Your approach and posted work are ok.

To continue,

$$3x+y=1\implies y=1-3x$$

$$3-xy=13\implies xy=-10$$

$$x(1-3x)=-10$$

$$(3x+5)(x-2)=0$$

$$(x,y)=\left(-\frac53,6\right),(2,-5)$$

Does that match your results?