SOLUTION: Solve the following system of equation: { 𝑿 + 𝟐𝒀 + 𝟑𝒁 = 𝟏𝟎 𝟐𝑿 − 𝒀 + 𝒁 = 𝟗 𝟑𝑿 − 𝒁 = 𝟑 }

Algebra ->  Equations -> SOLUTION: Solve the following system of equation: { 𝑿 + 𝟐𝒀 + 𝟑𝒁 = 𝟏𝟎 𝟐𝑿 − 𝒀 + 𝒁 = 𝟗 𝟑𝑿 − 𝒁 = 𝟑 }      Log On


   

Question 1155480: Solve the following system of equation:
{
𝑿 + 𝟐𝒀 + 𝟑𝒁 = 𝟏𝟎
𝟐𝑿 − 𝒀 + 𝒁 = 𝟗
𝟑𝑿 − 𝒁 = 𝟑
}
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x+%2B+2y+%2B+3z+=+10.......eq.1
2x+-+y+%2B+z+=+9.......eq.2
3x+-+z+=+3.......eq.3
------------------------------

3x+-+z+=+3.......eq.3...solve for z
z=3x+-+3.........eq.3a

2x+-+y+%2B+z+=+9.......eq.2...solve for z
+z+=-2x%2By%2B+9.......eq.2a

from eq.3a and eq.2a we have

3x+-+3=-2x%2By%2B+9......solve for y
y=3x+-+3%2B2x-9
y=5x+-+12........eq.b

go to

x+%2B+2y+%2B+3z+=+10.......eq.1, substitute y and z
x+%2B+2%285x+-+12%29+%2B+3%283x+-+3%29+=+10......solve for x
x+%2B+10x+-+24+%2B+9x+-+9+=+10
20x+-+33+=+10
20x+=+10%2B33
20x+=+43
highlight%28x+=+43%2F20%29

go to
y=5x+-+12........eq.b, substitute x
y=5%2843%2F20%29+-+12
y=43%2F4+-+12
y=43%2F4+-+48%2F4
highlight%28y=+-+5%2F4%29

go to

z=3x+-+3.........eq.3a, substitute x
z=3%2843%2F20%29+-+3
z=129%2F20+-+60%2F20
highlight%28z=69%2F20+%29