Question

How do you solve the system of equations `10x + 2y = 16` and `- 3x - 2y = - 9`?

Answer 1

See a solution process below:

Explanation:

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

`10x + 2y = 16`

`-color(red)(10x) + 10x + 2y = -color(red)(10x) + 16`

`0 + 2y = -10x + 16`

`2y = -10x + 16`

`(2y)/color(red)(2) = (-10x + 16)/color(red)(2)`

`(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = (-10x)/color(red)(2) + 16/color(red)(2)`

`y = -5x + 8`

Step 2) Substitute `(-5x + 8)` for `y` in the second equation and solve for `x`:

`-3x - 2y = -9` becomes:

`-3x - 2(-5x + 8) = -9`

`-3x + (-2 xx -5x) + (-2 xx 8) = -9`

`-3x + 10x + (-16) = -9`

`-3x + 10x - 16 = -9`

`(-3 + 10)x - 16 = -9`

`7x - 16 = -9`

`7x - 16 + color(red)(16) = -9 + color(red)(16)`

`7x - 0 = 7`

`7x = 7`

`(7x)/color(red)(7) = 7/color(red)(7)`

`(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = 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 + 8` becomes:

`y = (-5 xx 1) + 8`

`y = -5 + 8`

`y = 3`

The Solution Is: `x = 1` and `y = 3` or `(1, 3)`