Question

Please explain how to find the answer

Answer 1

`\rm x=(46)/(3)`

`\rm y=-(25)/(24)`

Explanation:

`\\ \Large \overline{ \rm - \: Steps \: using \: substitution \: - }`

`\rm (1)/(4)x+(4)/(5)y=3`

`\rm (1)/(4)x=-(4)/(5)y+3`

`\rm x=4\left(-(4)/(5)y+3\right)`

`\rm x=-(16)/(5)y+12`

┈

`\rm (5)/(16)\left(-(16)/(5)y+12\right)-(1)/(5)y=5`

`\rm -y+(15)/(4)-(1)/(5)y=5`

`\rm -(6)/(5)y+(15)/(4)=5`

`\rm -(6)/(5)y=(5)/(4)`

`\bold{ y=-(25)/(24)}`

┈

`\rm x=-(16)/(5)\left(-(25)/(24)\right)+12`

`\rm x=(10)/(3)+12`

`\bold{ x=(46)/(3)}`

Answer 2

• (46/3, - 25/24)

Explanation:

It is easier to solve it by elimination.

Add the first equation to 4 times the second one to eliminate y:

• 1/4x + 4/5y + 4*5/16x - 4/5y = 3 + 4*5
• 1/4x + 5/4x = 3 + 20
• 6/4x = 23
• 3/2x = 23
• x = 2*23/3
• x = 46/3

Now find y:

• 1/4*46/3 + 4/5y = 3
• 23/6 + 4/5y = 3
• 4/5y = 3 - 23/6
• 4/5y = -5/6
• y = -25/24