Question

A system of equations is shown below. y = –x – 3 5x + 2y = 9 What is the solution to this system?

Answer 1

`x=5\ and\ y=-8`

The solution of the system can be given as (5,-8).

Explanation:

Given system of equations:

`y=-x-3`

`5x+2y=9`

To solve the given system of equations:

Solution:

We will use substitution to solve the given system.

We will substitute the
`y` values in terms of
`x` from the equation
`y=-x-3` into the other equation to solve for
`x`

Substituting
`y=-x-3` into
`5x+2y=9`.

We have:

`5x+2(-x-3)=9`

Using distribution.

`5x-2x-6=9`

Combining like terms.

`3x-6=9`

Adding 6 both sides.

`3x-6+6=9+6`

`3x=15`

Dividing both sides by 3.

`(3x)/(3)=(15)/(3)`

∴
`x=5`

Plugging in
`x=5` into
`y=-x-3`.

We have,

`y=-5-3`

∴
`y=-8`

The solution of the system can be given as (5,-8).