Question

How do you solve the system of equations: `4x - y = 15` and `2x + 3y = 25`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve the second equation for `y`:

`4x - y = 15`

`-color(blue)(15) + 4x - y + color(red)(y) = -color(blue)(15) + 15 + color(red)(y)`

`-15 + 4x - 0 = 0 + y`

`-15 + 4x = y`

`y = 4x - 15`

Step 2) Substitute `(4x - 15)` for `y` in the first equation and solve for `x`:

`2x + 3y = 25` becomes:

`2x + 3(4x - 15) = 25`

`2x + (3 xx 4x) - (3 xx 15) = 25`

`2x + 12x - 45 = 25`

`(2 + 12)x - 45 = 25`

`14x - 45 = 25`

`14x - 45 + color(red)(45) = 25 + color(red)(45)`

`14x - 0 = 70`

`14x = 70`

`(14x)/color(red)(14) = 70/color(red)(14)`

`(color(red)(cancel(color(black)(14)))x)/cancel(color(red)(14)) = 5`

`x = 5`

Step 3) Substitute `5` for `x` in the solution to the second equation at the end of Step 1 and calculate `y`:

`y = 4x - 15` becomes:

`y = (4 xx 5) - 15`

`y = 20 - 15`

`y = 5`

The Solution Is: `x = 5` and `y = 5` or `(5, 5)`