What is 2x=a+b,4y=a-b,6z=a+2b,x+y+z=1,x-y+2z=2 ?

The solution to 2x=a+b,4y=a-b,6z=a+2b,x+y+z=1,x-y+2z=2 is

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2x=a+b,4y=a-b,6z=a+2b,x+y+z=1,x-y+2z=2

2 x = a + b, 4 y = a - b, 6 z = a + 2 b, x + y + z = 1, x - y + 2 z = 2

(x = \frac{18}{23}, y = - \frac{6}{23}, a = \frac{6}{23}, b = \frac{30}{23}, z = \frac{11}{23})

Solution steps

2 x = a + b 4 y = a - b 6 z = a + 2 b x + y + z = 1 x - y + 2 z = 2

Isolate

b

for

2 x = a + b : b = 2 x - a

Plug

b = 2 x - a

into

4 y = a - b

4 y = a - (2 x - a)

Simplify

4 y = 2 a - 2 x

Plug

b = 2 x - a

into

6 z = a + 2 b

6 z = a + 2 (2 x - a)

Simplify

6 z = - a + 4 x

4 y = 2 a - 2 x, 6 z = - a + 4 x, x + y + z = 1, x - y + 2 z = 2 : x = \frac{18}{23}, y = - \frac{6}{23}, a = \frac{6}{23}, z = \frac{11}{23}

Verify solutions by plugging them into the original equations

Therefore, the final solution for

2 x = a + b, 4 y = a - b, 6 z = a + 2 b, x + y + z = 1, x - y + 2 z = 2

(x = \frac{18}{23}, y = - \frac{6}{23}, a = \frac{6}{23}, b = \frac{30}{23}, z = \frac{11}{23})

- 4 x - 6 = - 3 x - 8

\frac{x}{3} + \frac{x}{2} + 5 = x

\frac{a x - 1}{a} + \frac{b x - 1}{b} = (2 - a - b) x

14 + x = 26

What is 2x=a+b,4y=a-b,6z=a+2b,x+y+z=1,x-y+2z=2 ?
The solution to 2x=a+b,4y=a-b,6z=a+2b,x+y+z=1,x-y+2z=2 is