Question

Given 3x - 2y = 8, a express x in terms of y and find x when y = 11, and b obtain a formula for y and find y when x = = 2.​

Answer 1

Hello!

Answer:

`\Large \boxed{\sf y =-4 + 1.5x }`

`\Large \boxed{\sf If ~y = 11, x ~=10}`

`\Large \boxed{\sf If ~x = 2, y ~=-1}`

Explanation:

→ We want:

- find x when y = 11

- obtain a formula for y

- find y when x = 2

→ We have this equation:

`\sf 3x - 2y = 8`

Find x when y = 11:

→ Let's replace y by 11 to find the value of x:

`\sf 3x - 2 * 11= 8`

→ Let's solve this equation to find x:

◼ Simplify the left side:

`\sf 3x - 22= 8`

◼ Add 22 to both sides:

`\sf 3x - 22+22= 8+22`

◼ Simplify both sides:

`\sf 3x =30`

◼ Divide both sides by 3:

`\sf (3x)/(3)= (30)/(3)`

◼ Simplify both sides:

`\boxed{\sf x = 10}`

Obtain a formula for y:

→ Let's solve y in this equation:

`\sf 3x - 2y = 8`

◼ Subtract 3x from both sides:

`\sf 3x - 2y -3x= 8-3x`

◼ Simplify both sides:

`\sf - 2y = 8-3x`

◼ Divide both sides by -2:

`\sf (- 2y)/(-2) = ( 8-3x)/(-2)`

◼ Simplify both sides:

`\boxed{\sf y =-4 + 1.5x }`

Find y when x = 2:

→ Let's replace x by 2 to find the value of y:

`\sf 3 * 2 - 2 y= 8`

→ Let's solve this equation to find y:

◼ Simplify the left side:

`\sf 6 - 2 y= 8`

◼ Subtract 6 from both sides:

`\sf 6 - 2 y-6= 8-6`

◼ Simplify both sides:

`\sf - 2 y= 2`

◼ Divide both sides by -2:

`\sf (-2y)/(-2) = (2)/(-2)`

◼ Simplify both sides:

`\boxed{\sf y = -1}`

Conclusion:

- In the equation 3x - 2y = 8, y is equal to -4 + 1.5x

- In the equation 3x - 2y = 8, if y = 11, x is equal to 10.

- In the equation 3x - 2y = 8, if x = 2, y is equal to -1.