Solve for x
x=\left(-\frac{1}{2}+\frac{1}{2}i\right)y+\left(\frac{1}{2}+\frac{1}{2}i\right)
Solve for y
y=\left(-1-i\right)x+i
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ix+iy=x-1
Use the distributive property to multiply x+y by i.
ix+iy-x=-1
Subtract x from both sides.
\left(-1+i\right)x+iy=-1
Combine ix and -x to get \left(-1+i\right)x.
\left(-1+i\right)x=-1-iy
Subtract iy from both sides.
\left(-1+i\right)x=-iy-1
Reorder the terms.
\frac{\left(-1+i\right)x}{-1+i}=\frac{-iy-1}{-1+i}
Divide both sides by -1+i.
x=\frac{-iy-1}{-1+i}
Dividing by -1+i undoes the multiplication by -1+i.
x=\left(-\frac{1}{2}+\frac{1}{2}i\right)y+\left(\frac{1}{2}+\frac{1}{2}i\right)
Divide -iy-1 by -1+i.
ix+iy=x-1
Use the distributive property to multiply x+y by i.
iy=x-1-ix
Subtract ix from both sides.
iy=\left(1-i\right)x-1
Combine x and -ix to get \left(1-i\right)x.
\frac{iy}{i}=\frac{\left(1-i\right)x-1}{i}
Divide both sides by i.
y=\frac{\left(1-i\right)x-1}{i}
Dividing by i undoes the multiplication by i.
y=\left(-1-i\right)x+i
Divide \left(1-i\right)x-1 by i.
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