Question

How do you solve the system of equations `y= 2x - 5` and `2y - 3x = 6`?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Because the first equation is already solved for `y`, substitute `2x - 5` for `y` in the second equation and solve for `x`:

`2y - 3x = 6` becomes:

`2(2x - 5) - 3x = 6`

`(2 xx 2x) - (2 xx 5) - 3x = 6`

`4x - 10 - 3x = 6`

`4x - 3x - 10 = 6`

`(4 - 3)x - 10 = 6`

`1x - 10 = 6`

`x - 10 = 6`

`x - 10 + color(red)(10) = 6 + color(red)(10)`

`x - 0 = 16`

`x = 16`

Step 2) Substitute `16` for `x` in the first equation and calculate `y`:

`y = 2x - 5` becomes:

`y = (2 xx 16) - 5`

`y = 32 - 5`

`y = 27`

The solution is: `x = 16` and `y = 27`