Solve x(4-5i)+y(2+6i)=-12-7i

$$x ( 4 - 5 i ) + y ( 2 + 6 i ) = - 12 - 7 i$$

Solve for x

$$x=\left(\frac{22}{41}-\frac{34}{41}i\right)y+\left(-\frac{13}{41}-\frac{88}{41}i\right)$$

Steps for Solving Linear Equation

Subtract y\left(2+6i\right) from both sides.

$$x\left(4-5i\right)=-12-7i-y\left(2+6i\right)$$

Multiply -1 and 2+6i to get -2-6i.

$$x\left(4-5i\right)=-12-7i+\left(-2-6i\right)y$$

The equation is in standard form.

$$\left(4-5i\right)x=\left(-2-6i\right)y+\left(-12-7i\right)$$

Divide both sides by 4-5i.

$$\frac{\left(4-5i\right)x}{4-5i}=\frac{\left(-2-6i\right)y+\left(-12-7i\right)}{4-5i}$$

Dividing by 4-5i undoes the multiplication by 4-5i.

$$x=\frac{\left(-2-6i\right)y+\left(-12-7i\right)}{4-5i}$$

Divide -12-7i+\left(-2-6i\right)y by 4-5i.

$$x=\left(\frac{22}{41}-\frac{34}{41}i\right)y+\left(-\frac{13}{41}-\frac{88}{41}i\right)$$

Solve for y

$$y=\left(\frac{11}{20}+\frac{17}{20}i\right)x+\left(-\frac{33}{20}+\frac{29}{20}i\right)$$

Steps for Solving Linear Equation

Subtract x\left(4-5i\right) from both sides.

$$y\left(2+6i\right)=-12-7i-x\left(4-5i\right)$$

Multiply -1 and 4-5i to get -4+5i.

$$y\left(2+6i\right)=-12-7i+\left(-4+5i\right)x$$

The equation is in standard form.

$$\left(2+6i\right)y=\left(-4+5i\right)x+\left(-12-7i\right)$$

Divide both sides by 2+6i.

$$\frac{\left(2+6i\right)y}{2+6i}=\frac{\left(-4+5i\right)x+\left(-12-7i\right)}{2+6i}$$

Dividing by 2+6i undoes the multiplication by 2+6i.

$$y=\frac{\left(-4+5i\right)x+\left(-12-7i\right)}{2+6i}$$

Divide -12-7i+\left(-4+5i\right)x by 2+6i.

$$y=\left(\frac{11}{20}+\frac{17}{20}i\right)x+\left(-\frac{33}{20}+\frac{29}{20}i\right)$$