Question

How do you solve the system of equations `2x - y = 12` and `4x + 5y = 10` by substitution?

Answer 1

`(5, -2)`

Explanation:

Given: `2x - y = 12 " and " 4x + 5y = 10`

To use substitution, one equation must be `x = " or " y =`. Solve for `y` in the first equation:

Add `y` to both sides: `" "2x = 12 + y`
Subtract `12` from both sides: `" " 2x - 12 = y`

Substitute `y = 2x - 12` into the second equation:

`4x + 5(2x - 12) = 10`

Distribute: `" "4x + 10x - 60 = 10`

Add like terms: `" "14x - 60 = 10`

Add `60` to both sides of the equation: `" "14x = 70`

Divide both sides by `14`: `x = 70/14 = 5; " " x = 5`

Substitute this into either equation and solve for `y`:

`y = 2(5) - 12 = 10 - 12 = -2`

CHECK:
`2(5) - (-2) = 12 " "`TRUE

`4(5) + 5(-2) = 20 - 10 = 10 " "` TRUE

The answer is the intersection between the two line equations:
`(5, -2)`