Question

2x+y-3z by y+3x =x by 2y. Find the value of z when x=1 and y=4

Answer 1

`\mathsf {z = (41)/(24)}`

Explanation:

`\textsf {Given :}`

`\mathsf {\frac {2x + y - 3z}{y + 3x} = (x)/(2y) }`

`\textsf {Substituting the values given (x = 1, y = 4) :}`

`\mathsf {\frac {2(1) + 4 - 3z}{4 + 3(1)} = (1)/(2(4)) }`

`\mathsf {\frac {6 - 3z}{7} = (1)/(8) }`

`\textsf {Cross multiply the values :}`

`\mathsf {8(6 - 3z) = 7}`

`\mathsf {48 - 24z = 7}`

`\mathsf {24z = 41}`

`\mathsf z = {(41)/(24)}`

Answer 2

`z=(41)/(24)`

Explanation:

Given equation:

`(2x + y - 3z)/(y + 3x) = (x)/(2y)`

Given:

• 
  `x=1`

• 
  `y=4`

Substitute the given values of x and y into the given equation:

`\implies (2(1) + 4 - 3z)/(4 + 3(1)) = (1)/(2(4))`

`\implies (6-3z)/(7)=(1)/(8)`

Cross multiply:

`\implies 8(6-3z)=7`

Expand the brackets:

`\implies 48-24z=7`

Subtract 48 from both sides:

`\implies -24z=-41`

Divide both sides by -24:

`\implies z=(41)/(24)`