Question

How do you solve `10x – 2y = 8 and 4x – 10y = -6`?

Answer 1

See a solution process below:

Explanation:

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

`10x - 2y = 8`

`(10x - 2y)/color(red)(-2) = 8/color(red)(-2)`

`(10x)/color(red)(-2) + (-2y)/color(red)(-2) = -4`

`-5x + (color(red)(cancel(color(black)(-2)))y)/cancel(color(red)(-2)) = -4`

`-5x + y = -4`

`color(red)(5x) - 5x + y = color(red)(5x) - 4`

`0 + y = 5x - 4`

`y = 5x - 4`

Step 3) Substitute `(5x - 4)` for `y` in the second equation and solve for `x`:

`4x - 10y = -6` becomes:

`4x - 10(5x - 4) = -6`

`4x - (10 xx 5x) + (-10 xx -4) = -6`

`4x - 50x + 40 = -6`

`(4 - 50)x + 40 = -6`

`-46x + 40 = -6`

`-46x + 40 - color(red)(40) = -6 - color(red)(40)`

`-46x + 0 = -46`

`-46x = -46`

`(-46x)/color(red)(-46) = (-46)/color(red)(-46)`

`(color(red)(cancel(color(black)(-46)))x)/cancel(color(red)(-46)) = 1`

`x = 1`

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

`y = 5x - 4` becomes:

`y = (5 xx 1) - 4`

`y = 5 - 4`

`y = 1`

The solution is: `x = 1` and `y = 1` or `(1, 1)`