Answer:
a) [tex]x = -1[/tex] and [tex]y = 5[/tex], b) [tex]x = 2[/tex] and [tex]y = -1[/tex], c) [tex]x = -2[/tex] and [tex]y = 1[/tex], d) [tex]x = 2[/tex] and [tex]y = -9[/tex], e) [tex]x = 2[/tex] and [tex]y = -2[/tex], f) [tex]x = 2[/tex] and [tex]y = -1[/tex], g) [tex]x = 2[/tex] and [tex]y = -1[/tex], h) [tex]x = 1[/tex] and [tex]y = 2[/tex].
Step-by-step explanation:
Each system is solved as follows (Cada sistema es resuelto como sigue):
a) [tex]2\cdot x + y = 3[/tex] and [tex]3\cdot x - y = -8[/tex]
[tex]y = 3 - 2\cdot x[/tex]
[tex]3\cdot x - 3 + 2\cdot x = -8[/tex]
[tex]5\cdot x = -5[/tex]
[tex]x = -1[/tex]
[tex]y = 5[/tex]
b) [tex]x - 2\cdot y = 4[/tex] and [tex]-x+3\cdot y = -5[/tex]
[tex]x = 4 + 2\cdot y[/tex]
[tex]-4-2\cdot y+3\cdot y = - 5[/tex]
[tex]-4+y = -5[/tex]
[tex]y = -1[/tex]
[tex]x = 2[/tex]
c) [tex]-2\cdot x + 5\cdot y = 9[/tex] and [tex]x - y = -3[/tex]
[tex]x = y-3[/tex]
[tex]-2\cdot y +6 +5\cdot y = 9[/tex]
[tex]3\cdot y = 3[/tex]
[tex]y = 1[/tex]
[tex]x = -2[/tex]
d) [tex]5\cdot x - 4\cdot y = 2[/tex] and [tex]3\cdot x + 2\cdot y = -12[/tex]
[tex]3\cdot x + 2\cdot y = -12[/tex]
[tex]6\cdot x + 4\cdot y = -24[/tex]
[tex]4\cdot y = -6\cdot x -24[/tex]
[tex]5\cdot x +6\cdot x +24 = 2[/tex]
[tex]11\cdot x = -22[/tex]
[tex]x = 2[/tex]
[tex]y = -9[/tex]
e) [tex]x + y = 0[/tex] and [tex]2\cdot x +3\cdot y = -2[/tex]
[tex]y = -x[/tex]
[tex]2\cdot x -3\cdot x = -2[/tex]
[tex]-x = -2[/tex]
[tex]x = 2[/tex]
[tex]y = -2[/tex]
f) [tex]3\cdot x + 5\cdot y = 1[/tex] and [tex]x + y = 1[/tex]
[tex]y = 1 - x[/tex]
[tex]3\cdot x + 5 - 5\cdot x = 1[/tex]
[tex]-2\cdot x = -4[/tex]
[tex]x = 2[/tex]
[tex]y = -1[/tex]
g) [tex]5\cdot x - 2\cdot y = 12[/tex] and [tex]4\cdot x + 3\cdot y = 5[/tex]
[tex]x = \frac{12+2\cdot y}{5}[/tex]
[tex]x = \frac{5-3\cdot y}{4}[/tex]
[tex]\frac{12+2\cdot y}{5} = \frac{5-3\cdot y}{4}[/tex]
[tex]4\cdot (12+2\cdot y) = 5\cdot (5-3\cdot y)[/tex]
[tex]48 + 8\cdot y = 25 - 15\cdot y[/tex]
[tex]23\cdot y = -23[/tex]
[tex]y = -1[/tex]
[tex]x = 2[/tex]
h) [tex]7\cdot x + 8\cdot y = 23[/tex] and [tex]3\cdot x + 2\cdot y = 7[/tex]
[tex]3\cdot x + 2\cdot y = 7[/tex]
[tex]12\cdot x + 8\cdot y = 28[/tex]
[tex]8\cdot y = 28 - 12\cdot x[/tex]
[tex]7\cdot x +28-12\cdot x = 23[/tex]
[tex]-5\cdot x = -5[/tex]
[tex]x = 1[/tex]
[tex]y = 2[/tex]
