Solve (x+y-1)+(5x-2y+23)i=0

$$( x + y - 1 ) + ( 5 x - 2 y + 23 ) i = 0$$

Solve for x

$$x=\left(\frac{9}{26}+\frac{7}{26}i\right)y+\left(-\frac{57}{13}-\frac{14}{13}i\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5x-2y+23 by i.

$$x+y-1+5ix-2iy+23i=0$$

Combine x and 5ix to get \left(1+5i\right)x.

$$\left(1+5i\right)x+y-1-2iy+23i=0$$

Combine y and -2iy to get \left(1-2i\right)y.

$$\left(1+5i\right)x+\left(1-2i\right)y-1+23i=0$$

Subtract \left(1-2i\right)y from both sides. Anything subtracted from zero gives its negation.

$$\left(1+5i\right)x-1+23i=\left(-1+2i\right)y$$

Add 1 to both sides.

$$\left(1+5i\right)x+23i=\left(-1+2i\right)y+1$$

Subtract 23i from both sides.

$$\left(1+5i\right)x=\left(-1+2i\right)y+1-23i$$

The equation is in standard form.

$$\left(1+5i\right)x=\left(-1+2i\right)y+\left(1-23i\right)$$

Divide both sides by 1+5i.

$$\frac{\left(1+5i\right)x}{1+5i}=\frac{\left(-1+2i\right)y+\left(1-23i\right)}{1+5i}$$

Dividing by 1+5i undoes the multiplication by 1+5i.

$$x=\frac{\left(-1+2i\right)y+\left(1-23i\right)}{1+5i}$$

Divide \left(-1+2i\right)y+\left(1-23i\right) by 1+5i.

$$x=\left(\frac{9}{26}+\frac{7}{26}i\right)y+\left(-\frac{57}{13}-\frac{14}{13}i\right)$$

Solve for y

$$y=\left(\frac{9}{5}-\frac{7}{5}i\right)x+\left(\frac{47}{5}-\frac{21}{5}i\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5x-2y+23 by i.

$$x+y-1+5ix-2iy+23i=0$$

Combine x and 5ix to get \left(1+5i\right)x.

$$\left(1+5i\right)x+y-1-2iy+23i=0$$

Combine y and -2iy to get \left(1-2i\right)y.

$$\left(1+5i\right)x+\left(1-2i\right)y-1+23i=0$$

Subtract \left(1+5i\right)x from both sides. Anything subtracted from zero gives its negation.

$$\left(1-2i\right)y-1+23i=\left(-1-5i\right)x$$

Add 1 to both sides.

$$\left(1-2i\right)y+23i=\left(-1-5i\right)x+1$$

Subtract 23i from both sides.

$$\left(1-2i\right)y=\left(-1-5i\right)x+1-23i$$

The equation is in standard form.

$$\left(1-2i\right)y=\left(-1-5i\right)x+\left(1-23i\right)$$

Divide both sides by 1-2i.

$$\frac{\left(1-2i\right)y}{1-2i}=\frac{\left(-1-5i\right)x+\left(1-23i\right)}{1-2i}$$

Dividing by 1-2i undoes the multiplication by 1-2i.

$$y=\frac{\left(-1-5i\right)x+\left(1-23i\right)}{1-2i}$$

Divide \left(-1-5i\right)x+\left(1-23i\right) by 1-2i.

$$y=\left(\frac{9}{5}-\frac{7}{5}i\right)x+\left(\frac{47}{5}-\frac{21}{5}i\right)$$