a) √2x+ 3y= 5 {obie strony mnożymy przez -√2} { 2x- √2y= √2 -2x -3√2y = -5√2 {dodajemy stronami} { 2x- √2y = √2 -4√2y = -4√2 /:(-4√2) { 2x- √2y= √2 y = 1 { 2x- √2*1= √2 y=1 { 2x - √2 = √2 /+( √2) y=1 { 2x = 2√2 y=1 { x = √2 Odp. x = √2 i y = 1 b) (√2-1)x + 3√2y= -√2 - 2 { (√2+1)x + 3y= 2√2 + 5 /*(-√2) {obie strony mnożymy przez -√2} (√2-1)x + 3√2y= -√2 - 2 { (-√2)*(√2+1)x + 3*(-√2)y= (2√2 + 5)*(-√2) (√2-1)x + 3√2y= -√2 - 2 {dodajemy stronami} { (-2 -√2)x - 3√2y= -4 - 5√2 (√2-1)x + (-2 -√2)x = -√2 - 2 -4 - 5√2 { (√2+1)x + 3y= 2√2 + 5 x(√2-1-2 -√2) = -6 -6√2 { (√2+1)x + 3y= 2√2 + 5 -3x = -6 -6√2 /:(-3) { (√2+1)x + 3y= 2√2 + 5 x = 2 + 2√2 {wstawiamy do drugiego równania} { (√2+1)x + 3y= 2√2 + 5 x = 2 + 2√2 { (√2+1)*(2 + 2√2) + 3y= 2√2 + 5 x = 2 + 2√2 { 2√2+ 4 + 2 + 2√2 + 3y= 2√2 + 5 x = 2 + 2√2 { 3y= 2√2 + 5 - 2√2- 4 -2 - 2√2 x = 2 + 2√2 { 3y= -1 - 2√2 /:3 x = 2+ 2√2 { y= ⁻⅓ - ⅔*√2 Odp. x= 2+ 2√2 i y= ⁻⅓ - ⅔*√2 c) 7x + 3y= 10¹⁴ /*(-2) { 14x - 4y= 10¹⁴ -14x - 6y = -2*10¹⁴ { 14x - 4y= 10¹⁴ -10y = - 10¹⁴ /:(-10) { 14x - 4y= 10¹⁴ y = 10¹³ { 14x - 4*10¹³ = 10¹⁴ y = 10¹³ { 14x = 10¹⁴ + 4*10¹³ y = 10¹³ { 14x = 14*10¹³ /:14 y = 10¹³ { x = 10¹³ Odp. x = 10¹³ i y = 10¹³
