Question

How do you solve the system of equations `10x - y = 30` and `3y + 5x = 50`?

Answer 1

See a solution process below:

Explanation:

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

`10x - y = 30`

`-color(red)(10x) + 10x - y = -color(red)(10x) + 30`

`0 - y = -10x + 30`

`-y = -10x + 30`

`-1 * -y = -1(-10x + 30)`

`y = (-1 * -10x) + (-1 * 30)`

`y = 10x - 30`

Step 2) Substitute `(10x - 30)` for `y` in the second equation and solve for `x`:

`3y + 5x = 50` becomes:

`3(10x - 30) + 5x = 50`

`(3 * 10x) - (3 * 30) + 5x = 50`

`30x - 90 + 5x = 50`

`30x + 5x - 90 = 50`

`(30 + 5)x - 90 = 50`

`35x - 90 = 50`

`35x - 90 + color(red)(90) = 50 + color(red)(90)`

`35x - 0 = 140`

`35x = 140`

`(35x)/color(red)(35) = 140/color(red)(35)`

`x = 4`

Step 3) Substitute `4` for `x` in the solution to the first equation at the end of Step 1 and calculate `y`:

`y = 10x - 30` becomes:

`y = (10 * 4) - 30`

`y = 40 - 30`

`y = 10`

The solution is: `x = 4` and `y = 10` or `(4, 10)`