Question

Help please i need this answer!!!!

how many solutions does the system have .
y = -2x - 4
y = 1/2x - 5

Answer 1

Answer: one solution

Explanation:

Pre-Solving

We are given the following system:

`y = -2x -4`

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

We want to find how many solutions it has.

A system can have one, infinetly many, or no solutions.

To find how many solutions the solution has, we can solve it.

Let's solve this system by substitution, as both systems are equal to y. This is possible via transitivity, where if a = b and b = c, then a = c.

Solving

Substitute -2x - 4 for y in
`y = (1)/(2)x -5`.

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

We can multiply both sides by 2 to clear the fraction.

-4x - 8 = x - 10

Add 4x to both sides.

-4x - 8 = x - 10

+4x +4x

______________________

-8 = 5x - 10

Add 10 to both sides.

-8 = 5x - 10

+10 +10

______________________
2 = 5x

Divide both sides by 5.

`(2)/(5) =x`

Now, substitute 2/5 as x in either
`y=-2x-4` or
`y = (1)/(2) x -5`.

Taking
`y = (1)/(2) x -5`, we get:

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

`y = (1)/(5) -5`

`y =- (24)/(5)`

The answer is:
`x = (2)/(5)`,
`y =- (24)/(5)`, or as a point, it's
`((2)/(5) ,- (24)/(5) )`.
As we can see, there is a solution to this system. This is the only solution to this system, so it has one solution.