You can put this solution on YOUR website! 5x-6y+4z=15
7x+4y-3z=19
2x+y+6z=46
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Isolate the x in 5x-6y+4z = 15:
5x=15+6y-4z
Divide both sides by 5:
x = (15+6y-4z)/5
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7x+4y-3z = 19 = 7((15+6y-4z)/5)+4y-3z=19
2x+y+6z = 46 = 2((15+6y-4z)/5)+y+6z = 46
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Isolate the y in 7((15+6y-4z)/5)+4y-3z=19:
7((15+6y-4z)/5)+4y-3z=19 rewrite: [7(15+6y-4z)]/5+4y-3z = 19
Multiply both sides times 5:
7(15+6y-4z)+20y-15z=95
105+42y-28z+20y-15z = 95
-43z+62y+105 = 95
62y+105 = 95+43z
62y = 43z-10
y = (43z-10)/62
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2((15+6(43z-10/62)-4z)/5)+(43z-10/62)+6z = 46
LCM of 5 and 62 is 310:
4(465+3(43z-10)-124z)+5(43z-10)+1860z=14260
= 2095z+1690=14260
= 2095z=12570
z = 12570/2095 = 6
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Now that we have z, let’s go back and find x and y:
y = (43z-10)/62
y = 43(6)-10/62 = 4
x = (15+6y-4z)/5
x= 15+6(4)-4(6)/5 = 3
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So there you have it:
x = 3
y = 4
z = 6
5x - 6y + 4z = 15 ------ eq (i)
7x + 4y - 3z = 19 ----- eq (ii)
2x + y + 6z = 46 ------ eq (iii)
12x + 6y + 36z = 276 ---------- Multiplying eq (iii) by 6 -------- eq (iv)
17x + 40z = 291 --------------- Adding eqs (iv) and (i) ---------- eq (v)
- 8x - 4y - 24z = - 184 ------- Multiplying eq (iii) by - 4 ------ eq (vi)
- x - 27z = - 165 ------------- Adding eqs (vi) and (ii) --------- eq (vii)
- 17x - 459z = - 2,805 -------- Multiplying eq (vii) by 17 ------- eq (viii)
- 419z = - 2,514 -------------- Adding eqs (viii) & (v)
- x - 27(6) = - 165 ----------- Substituting 6 for z in eq (vii)
- x - 162 = - 165
- x = - 165 + 162
- x = - 3
2(3) + y + 6(6) = 46 ---------- Substituting 3 for x, and 6 for z in eq (iii)
6 + y + 36 = 46
42 + y = 46
y = 46 - 42
I wonder who besides the other person who responded, would do the problem the way he did.
Who solves a system like this, by substitution, with all those MESSY, MESSY fractions? Get with it, and help the people the right way!
I get confused just looking at the way he did the problem! I'm sure others feel the same way!
