Question

Using substitution what is 5x-4y=-10 when y equals ​y=2x−5?

5x−4y=−10
​y=2x−5

Answer 1

See a solution process below:

Explanation:

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

`5x - 4y = -10` becomes:

`5x - 4(2x - 5) = -10`

`5x + (-4 xx 2x) + (-4 xx - 5) = -10`

`5x + (-8x) + 20 = -10`

`5x - 8x + 20 = -10`

`(5 - 8)x + 20 = -10`

`-3x + 20 = -10`

`-3x + 20 - color(red)(20) = -10 - color(red)(20)`

`-3x + 0 = -30`

`-3x = -30`

`(-3x)/color(red)(-3) = (-30)/color(red)(-3)`

`(color(red)(cancel(color(black)(-3)))x)/cancel(color(red)(-3)) = 10`

`x = 10`

Step 2) Substitute `10` for `x` in the second equation and calculate `y`

`y = 2x - 5` becomes:

`y = (2 xx 10) - 5`

`y = 20 - 5`

`y = 15`

The Solution Is: `x = 10` and `y = 15` or `(10, 15)`