Question

How do solve the following linear system?: `-7x + y = -19 , -2x + 3y = -19`?

Answer 1

`x=2` and `y=-5`

Explanation:

For a linear system with 2 different unknowns, we use
Substitution Equation to find the actual value of the unknown.

There are two unknowns, `x` and `y`.

Firstly, let `-7x+y=-19` as Equation 1
and `-2x+3y=-19` as Equation 2.

From one of the equation, for example Equation 1 we can rearrange a new equation and substitute it into the other equation.

Let say, from Equation 1,
`-7x+y=-19`
Rearrange the equation in terms of only one unknown.
`y=-19+7x` as Equation 3

Substitute Equation 3 into Equation 2 and we will get;
`-2x+3y=-19` given `y=-19+7x`,

`-2x+3(-19+7x)=-19`

`-2x-57+21x=-19`

`-2x+21x=-19+57`

`19x=38`

`x=2`

Substitute `x=2` into Equation 3 and we will get;
`y=-19+7x` given `x=2`

`y=-19+7(2)`

`y=-5`