Question

How do you find the solution of the system of equations `4x - 5y = 40` and `2x + 10y=20`?

Answer 1

See a solution process below:

Explanation:

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

`2x + 10y = 20`

`2x + 10y - color(red)(10y) = 20 - color(red)(10y)`

`2x + 0 = 20 - 10y`

`2x = 20 - 10y`

`(2x)/color(red)(2) = (20 - 10y)/color(red)(2)`

`x = 20/color(red)(2) - (10y)/color(red)(2)`

`x = 10 - 5y`

Step 3) Substitute `(10 - 5y)` for `x` in the first equation and solve for `y`:

`4x - 5y = 40` becomes:

`4(10 - 5y) - 5y = 40`

`(4 xx 10) - (4 xx 5y) - 5y = 40`

`40 - 20y - 5y = 40`

`40 + (-20 - 5)y = 40`

`40 + (-25)y = 40`

`40 - 25y = 40`

`40 - color(red)(40) - 25y = 40 - color(red)(40)`

`0 - 25y = 0`

`-25y = 0`

`(-25y)/color(red)(-25) = 0/color(red)(-25)`

`y = 0`

Step 3) Substitute `0` for `y` in the solution to the second equation at the end of Step 1 and calculate `x`:

`x = 10 - 5y` becomes:

`x = 10 - (5 xx 0)`

`x = 10 - 0`

`x = 10`

The Solution Is:

`x = 10` and `y = 0`

Or

`(10, 0)`

Answer 2

Here's the solution graphically:

#graph{(4x-5y-40)(2x+10y-20)=0[-5,15,-5,5]}