Question

6. Rezolvați următoarele sisteme:
(4x-3y=3
a)
5x - 4y=-1
b)
2(2x - y-5)-3(x – 2y-3) = 9
13(2x + 3y + 5) – 2(4x + 5y +6)=4​

Answer 1

Răspuns:

$a)4x - 3y = 3 | \times 4 \\ 5x - 4y = 1 | \times ( - 3) \\ 16x - 12y = 12 \\ - 15x + 12y = - 3 \\ 16x + ( - 15x) - 12y + 12y = 12 - 3 \\ x = 12 - 3 = 9 \\ \\ 16 \times 9 - 12y = 12 \\ 144 - 12y = 12 \\ 12y = 132 \: \: y = 11$

$b)2(2x - y - 5) - 3(x - 2y - 3) = 9 \\ 13(2x + 3y + 5) - 2(4x + 5y + 6) = 4 \\ 4x - 2y - 10 - 3x + 6y + 9 = 9 \\ 26x + 39y + 65 - 8x - 10y - 12 = 4 \\ x + 4y - 1 = 9 | \times ( - 18) \\ 18x + 29y + 53 = 4 \\ - 18x - 72y + 18 = - 162 \\ 18x + 29y + 53 = 4 \\ - 18x + 18x - 72y + 29y + 18 + 53 = - 162 + 4 \\ - 43y + 71 = - 158 \\ - 43y = - 229 \\ y = \frac{229}{43}$