Question

Solve the equation 16x+9=9y-2x for y.

Answer 1

GIVEN:

We are given the following equation;

`16x+9=9y-2x`

Required;

Solve the equation for y.

Step-by-step solution;

To solve, we simply collect like terms as follows;

`\begin{gathered} Add\text{ }2x\text{ }to\text{ }both\text{ }sides: \\ 16x+2x+9=9y-2x+2x \end{gathered}`

We now have;

`18x+9=9y`

Observe that -2x and +2x cancel out each other on the right hand side.

Next step, we divide both sides by 9, that is the coefficient of y.

`(18x+9)/(9)=(9y)/(9)`
`(18x+9)/(9)=y`

Note that we can split up the left hand side. We do this by taking both numbers in the numerator and writing each as a fraction with 9 as the denominator. This is because 9 is the LCM of both fractions as it is expressed above.

We now have;

`(18x)/(9)+(9)/(9)=y`

Now we divide both fractions by any common factors;

`2x+1=y`

Therefore,

ANSWER:

`y=2x+1`