Ответ:

1)

[tex]\left \{ {{3x-7y=11} \atop {6x+7y =16}} \right. \\9x = 27\\x=3\\3*3-7y=11\\9-7y=11\\7y = -2\\y = -\frac{2}{7}[/tex]

2)

[tex]\left \{ {{4x+2y=5} \atop {4x-6y=-7}} \right. \\\left \{ {{12x+6y=15} \atop {4x-6y=-7}} \right. \\16x = 8\\x = \frac{1}{2} = 0.5\\4*0.5 -6y = -7\\2-6y = -7\\6y = 9\\y = \frac{9}{6} = 1.5[/tex]

3)

[tex]\left \{ {{2x-3y=8} \atop {7x-5y=-5}} \right. \\\left \{ {{10x-15y=40} \atop {-21x+15y=15}} \right. \\-11x = 55\\x = -5\\2*(-5) - 3y = 8\\-10-3y = 8\\3y = -18\\y = -6[/tex]

4)

y = kx+b

M(3;1)

E( 1; 5)

[tex]\left \{ {{1=3k+b} \atop {5=k+b}} \right. \\[/tex]

вычтем из первого второе

[tex]-4=2k\\k = -2\\1=3*(-2)+b\\1 = -6+b\\b = 7[/tex]

k = -2

b= 7

y = -2x+7