How do you solve the system of equations 4x+2y+z=7, 2x+2y+4z=-4, x+3y-2z=-84x+2y+z=7,2x+2y+4z=−4,x+3y−2z=−8?
1 Answer
x=47/11x=4711
y=(-51)/11y=−5111
z=(-9)/11z=−911
Explanation:
Given -
4x+2y+z=74x+2y+z=7 ----------------(1)
2x+2y+4z=-42x+2y+4z=−4 -------------(2)
x+3y-2z=-8x+3y−2z=−8 ----------------(3)
Take the first two equations and eliminate
4x+2y+z=74x+2y+z=7 ----------------(1)
2x+2y+4z=-42x+2y+4z=−4 -------------(2) --------(1)-(2)(1)−(2)
2x-3z=112x−3z=11 -------------(4)
Take equations (1) and (3)
We have to elimiate
4x+2y+z=74x+2y+z=7 ----------------(1) -------xx3×3
x+3y-2z=-8x+3y−2z=−8 ----------------(3) -------xx2×2
12x+6y+3z=2112x+6y+3z=21 ------------(5)
2x+6y-4z=-162x+6y−4z=−16 -------------(6) -----(5)-(6)(5)−(6)
10x+7z=3710x+7z=37 ----------------(7)
Take equations (4) and (7)
2x-3z=112x−3z=11 -------------(4) --------xx5×5
10x+7z=3710x+7z=37 ----------------(7)
10x-15z=5510x−15z=55 ---------(8)
10x+7z=3710x+7z=37 -----------(7) ------(8)-(7)(8)−(7)
-22z=18−22z=18
z=-18/22z=−1822
Plugin >
10x+7(-18/22)=3710x+7(−1822)=37
10x-126/22=3710x−12622=37
10x=37+126/22=(814+126)/22=940/22=470/1110x=37+12622=814+12622=94022=47011
x=470/11xx1/10=470/110=47/11x=47011×110=470110=4711
x=47/11x=4711
Plugin >
4x+2y+z=74x+2y+z=7 ----------------(1)
4(47/11)+2y-18/22=74(4711)+2y−1822=7
4(47/11)+2y-9/11=74(4711)+2y−911=7
188/11+2y-9/11=718811+2y−911=7
(188-9)/11+2y=7188−911+2y=7
179/11+2y=717911+2y=7
2y=7-179/11=(77-179)/11=(-102)/112y=7−17911=77−17911=−10211
y=(-102)/11xx1/2=(-102)/22=y=−10211×12=−10222=
y=(-51)/11y=−5111
x=47/11x=4711
y=(-51)/11y=−5111
z=-18/22=(-9)/11z=−1822=−911