Question

What is the solution to the system of equations below? y = one-half x minus 4 and y = negative 2 x minus 9 (–2, –5) (–2, –3) (2, –3) (2, –13)

Answer 1

is A: (–2, –5)

Explanation:

i took the test and got it right

Answer 2

We have been given a system of equations
`y=(1)/(2)x-4` and
`y=-2x-9`. We are asked to find the solution of our given system of equations.

To solve our system of equations, we will equate both equations as:

`(1)/(2)x-4=-2x-9`

`(1)/(2)x-4+4=-2x-9+4`

`(1)/(2)x=-2x-5`

`(1)/(2)x+2x=-2x+2x-5`

`(1)/(2)x+(4)/(2)x=-5`

`(1+4)/(2)x=-5`

`(5)/(2)x=-5`

`(2)/(5)\cdot (5)/(2)x=-5\cdot (2)/(5)`

`x=-2`

Upon substituting
`x=-2` in equation
`y=-2x-9`, we will get:

`y=-2(-2)-9`

`y=4-9`

`y=-5`

Therefore, the solution of our given system of equations would be
`(-2,-5)` and option A is the correct choice.