Question

How do you solve the following system: # 3x – 5y = 53 , 4x+y=10 #?

Answer 1

See the entire solution process below:

Explanation:

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

`4x + y = 10`

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

`0 + y = -4x + 10`

`y = -4x + 10`

Step 2) Substitute `-4x + 10` for `y` in the first equation and solve for `x`:

`3x - 5y = 53` becomes:

`3x - 5(-4x + 10) = 53`

`3x - (5 * -4x) - (5 * 10) = 53`

`3x - (-20x) - 50 = 53`

`3x + 20x - 50 = 53`

`23x - 50 = 53`

`23x - 50 + color(red)(50) = 53 + color(red)(50)`

`23x - 0 = 103`

`23x = 103`

`(23x)/color(red)(23) = 103/color(red)(23)`

`(color(red)(cancel(color(black)(23)))x)/cancel(color(red)(23)) = 103/23`

`x = 103/23`

Step 3) Substitute `103/23` for `x` in the solution to the second equation at the end of Step 1 and calculate `y`

`y = -4x + 10` becomes:

`y = (-4 * 103/23) + 10`

`y = -412/23 + (10 * 23/23)`

`y = -412/23 + 230/23`

`y = -182/23`

The solution is: `x = 103/23` and `y = -182/23`