What is 2x+y-2z=10,3x+2y+2z=1,5x+4y+3z=4 ?

The solution to 2x+y-2z=10,3x+2y+2z=1,5x+4y+3z=4 is x=1,y=2,z=-3

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2x+y-2z=10,3x+2y+2z=1,5x+4y+3z=4

2 x + y - 2 z = 10, 3 x + 2 y + 2 z = 1, 5 x + 4 y + 3 z = 4

x = 1, y = 2, z = - 3

Solution steps

2 x + y - 2 z = 10 3 x + 2 y + 2 z = 1 5 x + 4 y + 3 z = 4

Isolate

x

for

2 x + y - 2 z = 10 : x = \frac{10 - y + 2 z}{2}

Substitute

x = \frac{10 - y + 2 z}{2}

[3 \cdot \frac{10 - y + 2 z}{2} + 2 y + 2 z = 1 5 \cdot \frac{10 - y + 2 z}{2} + 4 y + 3 z = 4]

Simplify

[\frac{y + 10 z + 30}{2} = 1 \frac{3 y + 16 z + 50}{2} = 4]

Isolate

y

for

\frac{y + 10 z + 30}{2} = 1 : y = - 10 z - 28

Substitute

y = - 10 z - 28

[\frac{3 ( - 10 z - 28 ) + 16 z + 50}{2} = 4]

Simplify

[- 7 z - 17 = 4]

Isolate

z

for

- 7 z - 17 = 4 : z = - 3

For

y = - 10 z - 28

Substitute

z = - 3

y = - 10 (- 3) - 28

- 10 (- 3) - 28 = 2

y = 2

For

x = \frac{10 - y + 2 z}{2}

Substitute

y = 2, z = - 3

x = \frac{10 - 2 + 2 ( - 3 )}{2}

\frac{10 - 2 + 2 ( - 3 )}{2} = 1

x = 1

The solutions to the system of equations are:

x = 1, y = 2, z = - 3

m + n = 1, 2 m - n = 4

x + y = 3, x - y = 4

2 x + 3 r = 2, 2 x - 3 y = 0

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

x + 4 y = 3, x + 2 y = 5

What is 2x+y-2z=10,3x+2y+2z=1,5x+4y+3z=4 ?
The solution to 2x+y-2z=10,3x+2y+2z=1,5x+4y+3z=4 is x=1,y=2,z=-3