Question 1097642

x/6+y/2+z/6=1/2
x+y+z=5
x/3+y/2+z/6=1
<pre>{{{x/6 + y/2 + z/6 = 1/2}}} ------- eq (i)
{{{x + y + z = 5}}} ------- eq (ii)
{{{x/3 + y/2 + z/6 = 1}}} ------- eq (iii)
 x + 3y + z = 3 ----- Multiplying eq (i) by LCD, 6 ------- eq (iv)
 x +  y + z = 5 ----- eq (ii)
2x + 3y + z = 6 ----- Multiplying eq (iii) by LCD, 6 ----- eq (v)

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2y = - 2 ----- Subtracting eq (ii) from eq (iv)
{{{highlight_green(matrix(1,5, y, "=", (- 2)/2, "=", - 1))}}}

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{{{highlight_green(matrix(1,3, x, "=", 3))}}} ----- Subtracting eq (v) from eq (iv)

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3 + - 1 + z = 5 ----- Substituting 3 for x, and - 1 for y in eq (ii) 
{{{highlight_green(matrix(1,5, z, "=", 5 - 2, "=", 3))}}}</pre>