Question

How do you solve the system of equations `2x+3y=16` and `5x-2y=21`?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Solve the first equation for `x`:

`2x + 3y = 16`

`2x + 3y - color(red)(3y) = 16 - color(red)(3y)`

`2x + 0 = 16 - 3y`

`2x = 16 - 3y`

`(2x)/color(red)(2) = (16 - 3y)//color(red)(2)`

`x = 8 - 3/2y`

Step 2) Substitute `8 - 3/2y` for `x` in the second equation and solve for `y`:

5(8 - 3/2y) - 2y = 21#

`40 - 15/2y - 2y = 21`

`40 - 15/2y - (2/2 xx 2)y = 21`

`40 - 15/2y - 4/2y = 21`

`40 - 19/2y = 21`

`40 - color(red)(40) - 19/2y = 21 - color(red)(40)`

`0 - 19/2y = -19`

`-19/2y = -19`

`-2/19 xx -19/2y = -2/19 xx -19`

`38/38y = 2`

`y = 2`

Step 3) Substitute `2` for `y` in the solution for the first equation at the end of Step 1 and calculate `x`:

`x = 8 - (3/2 xx 2)`

`x = 8 - 3`

`x = 5`

The solution is `x = 5` and `y = 2`