Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# solve the following linear equations ?

x- 2y + 3z = 7

2x + y + z = 4

-3x + 2y - 2z = -10

Relevance
• 3 weeks ago

2y - 2z = -10+3x, y + z = 4 - 2x, x = 7 + 2y - 3z

y(x) = ( (-10+3x)×1+2×(4 - 2x) ) / (2×1+2×1) = -(x + 2)/4z(x) = ( 2×(4 - 2x) - (-10+3x)×1) / (2×1+2×1) = (-7x + 18)/4

x = 7 + 2y - 3z = 7 + 2(-(x + 2)/4) - 3(-7x + 18)/4 = (19 x - 30)/4 = 2

y = -(2 + 2)/4 = -1

z = (-7×2 + 18)/4 = 1

Solution: (2, -1, 1)

• 1 month ago

x-2y+3z=7-------(1)

2x+y+z=4--------(2)

-3x+2y-2z=-10--(3)

=>

x=2

y=-1

z=1

directly from my own software.

Handy solution:

(1)+(3)=>

-2x+z=-3------(4)

-2(2)+(3)=>

7x+4z=18----(5)

-4(4)+(5)=>

15x=30

=>

x=2

z=1 from (4)

y=4-4-1=-1 from (2)

• 1 month ago

{z = -x/3 + (2 y)/3 + 7/3, z = -2 x - y + 4, z = -(3 x)/2 + y + 5}

x = 2,  y = -1,  z = 1

• 1 month ago

x - 2y + 3z = 7

2x + y + z = 4

-3x + 2y - 2z = -10

5x + 5z = 15

• 1 month ago

If we have three equations in three unknowns, we need to combine them to get two equations in two unknowns.

2(2) + (1) => 5x + 5z = 15

i.e. x + z = 3...(4)

2(2) - (3) => 7x + 4z = 18...(5)

(4) into (5) for x gives:

7x + 4(3 - x) = 18

so, 3x + 12 = 18

Hence, x = 2

Then, z = 1 => y = -1

Therefore, (x, y, z) => (2, -1, 1)

:)>

• 1 month ago

x- 2y + 3z = 7  ............................. (1)

2x + y + z = 4   ..............................(2)

-3x + 2y - 2z = -10  .......................(3)

From (1) :  x  =  2 y - 3 z + 7 .............................. (a)

Substitute this value one by one in eqns (2) and (3)  and siplify -

=>  2 (2 y - 3 z + 7) + y + z  =  4      ...   from (2)

=> 5 y - 5 z  =  - 10

=>  y - z  =  - 2    ................................ (3)

Again from (3) we get -

=>  - 3 (2 y - 3 z + 7) + 2 y - 2 z  =  - 10

=>  - 4 y + 7 z  =   11   .............. (4)

Now solving simultaneous eqns (3) and (4) :

y  =  - 1 and z  =  + 1

Substituting these values in (a) above :

x  =  2 ( - 1 ) - 3 ( 1 )  +  7

=>  x  =  - 2 - 3 + 7  =  2

================================

Answer :  x  =  + 2,  y  =  - 1  and z = + 1

\================================

• 1 month ago

Double equation 2:

4x + 2y + 2z = 8

5x + 5z = 15

Divide that by 5:

x + z = 3, so z = 3 - x

-2x + z = -3

Substitute z = 3 - x into that:

-2x + 3 - x = -3

-3x = -3 - 3

-3x = -6

x = (-6)/(-3) = 2

Substitute that into z = 3 - x:

z = 3 - 2 = 1

Substitute x and z into equation 2:

2*2 + y + 1 = 4

4 + y + 1 = 4

y = 4 - 4 - 1

y = -1

• 1 month ago

I agree with anonymous.

mathway helps with math

x=2

y=-1

z=1

• Anonymous
1 month ago

mathway.com. stupid