Answer:

Solve equation [3] for the variable d

[3] d = -4a + 4b - C + 9

// PLUG this in for variable d in equation [1]

[1] 2a + b - 5c + 3•(-4a+4b-c +9) = 35

[1] -10a + 13b - 8c = 8

// Plug this in for variable d in equation [2]

[2] a - 3b - c + 4•(-4a+4b-c +9) = 8

[2] -15a + 13b - 5c = -28

// Plug this in for variable d in equation [4]

[4] -a + 2b - 3c + 2•(-4a+4b-c +9) = 14

[4] -9a + 10B - 5c = -4

// Solve equation [4] for the variable b

[4] 10b = 9a + 5c - 4

[4] b = 9a/10 + c/2 - 2/5

// Plug this in for variable b in equation [1]

[1] -10a + 13•(9a/10+c /2-2/5) - 8c = 8

[1] 17a/10 - 3c/2 = 66/5

[1] 17a - 15c = 132

// Plug this in for variable b in equation [2]

[2] -15a + 13•(9a/10+c /2-2/5) - 5c = -28

[2] -33a/10 + 3c/2 = -114/5

[2] -33a + 15c = -228

// Solve equation [2] for the variable c

[2] 15c = 33a - 228

[2] c = 11a/5 - 76/5

// Plug this in for variable c in equation [1]

[1] 17a - 15•(11a/5-76/5) = 132

[1] -16a = -96

// Solve equation [1] for the variable a

[1] 16a = 96

[1] a = 6

// By now we know this much :

a = 6

b = 9a/10+c/2-2/5

c = 11a/5-76/5

d = -4a+4b-c+9