Solve (2+3i)x+(5+4i)y=49-11i

$$( 2 + 3 i ) x + ( 5 + 4 i ) y = 49 - 11 i$$

Solve for x

$$x=\left(-\frac{22}{13}+\frac{7}{13}i\right)y+\left(5-13i\right)$$

Steps for Solving Linear Equation

Subtract \left(5+4i\right)y from both sides.

$$\left(2+3i\right)x=49-11i-\left(5+4i\right)y$$

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

$$\left(2+3i\right)x=49-11i+\left(-5-4i\right)y$$

The equation is in standard form.

$$\left(2+3i\right)x=\left(-5-4i\right)y+\left(49-11i\right)$$

Divide both sides by 2+3i.

$$\frac{\left(2+3i\right)x}{2+3i}=\frac{\left(-5-4i\right)y+\left(49-11i\right)}{2+3i}$$

Dividing by 2+3i undoes the multiplication by 2+3i.

$$x=\frac{\left(-5-4i\right)y+\left(49-11i\right)}{2+3i}$$

Divide 49-11i+\left(-5-4i\right)y by 2+3i.

$$x=\left(-\frac{22}{13}+\frac{7}{13}i\right)y+\left(5-13i\right)$$

Solve for y

$$y=\left(-\frac{22}{41}-\frac{7}{41}i\right)x+\left(\frac{201}{41}-\frac{251}{41}i\right)$$

Steps for Solving Linear Equation

Subtract \left(2+3i\right)x from both sides.

$$\left(5+4i\right)y=49-11i-\left(2+3i\right)x$$

Multiply -1 and 2+3i to get -2-3i.

$$\left(5+4i\right)y=49-11i+\left(-2-3i\right)x$$

The equation is in standard form.

$$\left(5+4i\right)y=\left(-2-3i\right)x+\left(49-11i\right)$$

Divide both sides by 5+4i.

$$\frac{\left(5+4i\right)y}{5+4i}=\frac{\left(-2-3i\right)x+\left(49-11i\right)}{5+4i}$$

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

$$y=\frac{\left(-2-3i\right)x+\left(49-11i\right)}{5+4i}$$

Divide 49-11i+\left(-2-3i\right)x by 5+4i.

$$y=\left(-\frac{22}{41}-\frac{7}{41}i\right)x+\left(\frac{201}{41}-\frac{251}{41}i\right)$$