Bloom asked in Science & MathematicsMathematics · 6 months ago

# System of equations problem?

What is

−x+y+z=2,4x−3y−z=−3, x+y+z=8

Relevance
• 6 months ago

❶: −x+y=2-z, ❷: x+y=8-z, and ❸: z=3+4x−3y

From ❶ and ❷:

❹: x = ((2-z)×1-1×(8-z))/(-1×1-1×1) = 3 (𝑥 𝑠𝑜𝑙𝑣𝑒𝑑)

❺: y = (-1×(8-z)-(2-z)×1)/(-1×1-1×1) = 5-z

From ❸, ❹, and ❺:

❻: z = 3+4×3−3(5-z) = 3z = 0 (𝑧 𝑠𝑜𝑙𝑣𝑒𝑑)

From ❺ and ❻:

❼: y = 5-0 = 5 (𝑦 𝑠𝑜𝑙𝑣𝑒𝑑)

Solution: x=3, y=5, z=0

• Philip
Lv 6
6 months ago

-x  +y+ z =  2...(1).

4x -3y - z = -3...(2).

x  +y + z =  8...(3).

[(1)+(3)]--->  y  + z = 5...(4).

[(2)+4(1)]--> y +3z = 5...(5).

[(5)-(4)]-----> 2z = 0, ie., z = 0...(6).

[(4)-(6)]---> y = 5.

(3)---> x = 8 - (y+z) = (8-5) = 3.

Then (x,y,z) = (3,5,0).

• Ash
Lv 7
6 months ago

−x+y+z=2 ..................(1)

4x−3y−z=−3  .............(2)

x+y+z=8   ...................(3)

−x+y+z + x+y+z = 2+8

2y+2z = 10

y+z = 5 .............(4)

Add (2) to 4 times (1)

4x−3y−z + 4(−x+y+z) = -3 + 4(2)

4x−3y−z -4x + 4y + 4z = 5

y + 3z = 5 ...........(5)

Subtract (4) from (5)

y + 3z - (y+z) = 5 - 5

y + 3z -y - z = 0

2z = 0

z = 0

plug in (4)

y + 0 = 5

y = 5

plug value of y and z in (1)

-x + 5 + 0 = 2

-x = -3

x = 3

x = 3, y = 5, z = 0