Question 1132289

2x+y-2z=10;3x+2y+2z=1; 5x+4y+3z=4 
solve .
<pre>2x + y - 2z = 10 -------- eq (i)
3x + 2y + 2z = 1 -------- eq (ii)
5x + 4y + 3z = 4 -------- eq (iii) 
6x + 4y + 4z = 2 -------- Multiplying eq (ii) by 2 ----- eq (iv)
x + z = - 2 ------ Subtracting eq (iii) from (iv) ------ eq (v)
- 4x - 2y + 4z = - 20 --- Multiplying eq (i) by - 2 ---- eq (vi)
- x + 6z = - 19 --------- Adding eqs (vi) & (ii) ------- eq (vii)
7z = - 21 ---------- Adding eqs (vii) & (v)
{{{highlight_green(matrix(1,5, z, "=", (- 21)/7, "=", - 3))}}}

x - 3 = - 2 -------- Substituting - 3 for z in eq (v)
{{{highlight_green(matrix(1,5, x, "=", - 2 + 3, "=", 1))}}}

2(1) + y - 2(- 3) = 10 ------- Substituting 1 for x, and - 3 for z in eq (i) 
2 + y + 6 = 10
{{{highlight_green(matrix(1,5, y, "=", 10 - 8, "=", 2))}}}