Question

2. Rezolvati prin metoda substitutiei sistemelor : a) 3 supra 5x+1 supra 2y =2 ; -7x+4y=-43 b) √2x-3y=-7 ; x+4y=√2+12 c) x+√7y =12 ; -3x+2√7y =-1

Answer 1

a) 3x/5+y/2 =2     
 -7x+4y=-43   

6x+5y=20    y=(20-6x)/5
 -7x+4y=-43   
-7x+4(20-6x)/5=-43
-35x+80-24x=-215
-59x=-295
x=5
y=(20-6×5)/5=(20-30)/5=-2

b) √2x-3y=-7
 x+4y=√2+12
x=√2+12 -4y
√2(√2+12 -4y)-3y=-7
2+12√2-4√2y-3y=-7
y(3+4√2)=9+12√2
y(3+4√2)=3(3+4√2)
y=3
x=√2+12 -4×3=√2+12 -12=√2

c) x+√7y =12        x=12-√7y
 -3x+2√7y =-1
-3(12-√7y)+2√7y=-1
-36+3√7y+2√7y=-1
5√7y=35
y=35/5√7=7/√7=√7
x=12-√7×√7=12-7=5