Solve the following equations for real x and y.(2-3i)(x+yi) = 4+i

Answer:see explanationStep-by-step explanation:Expand the left side and equate to like terms on the right side(2 - 3i)(x + yi)= 2x + 2iy - 3ix - 3yi² ← using i² = - 1, then= 2x + 2iy - 3ix + 3y → compare with 4 + i2x + 3y = 4 → (1)- 3x + 2y = 1 → (2)Multiply (1) by 3 and (2) by 26x + 9y = 12 → (3)- 6x + 4y = 2 → (4)Add (3) and (4) term by term to eliminate term in x13y = 14 ( divide both sides by 13 )y = [tex]\frac{14}{13}[/tex]Substitute this value into (1) and solve for x2x + [tex]\frac{42}{13}[/tex] = [tex]\frac{52}{13}[/tex]Subtract [tex]\frac{42}{13}[/tex] from both sides2x = [tex]\frac{10}{13}[/tex] ← divide both sides by 2x = [tex]\frac{5}{13}[/tex]Hence x = [tex]\frac{5}{13}[/tex] and y = [tex]\frac{14}{13}[/tex]