Question

How do you solve the system of equations: `8x + 10y = 280; 2x + 4y = 100`?

Answer 1

`x = 10` and `y = 20`

Explanation:

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

`2x + 4y - 4y = 100 - 4y`

`2x = 100 - 4y`

`1/2 * 2x = 1/2(100 - 4y)`

`x = 50 - 2y`

Step 2) Substitute `50 - 2y` for `x` in the first equation and solve for `y`:

`8(50 - 2y) + 10y = 280`

`400 - 16y + 10y = 280`

`400 - 6y = 280`

`400 - 400 - 6y = 280 - 400`

`-6y = -120`

`(-6y)/(-6) = (-120)/(-6)`

`y = 20`

Step 3) Substitute `20` for `y` in the solution to the second equation in Step 1) and calculate `x`:

`x = 50 - 2*20`

`x = 50 - 40`

`x = 10`