johnsonkyaira
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ILL GIVE BRAINLIEST!!!!
What is the solution to the system of equations below?
y = 1/2x - 4 and y = -2x - 9
(–2, –5) (–2, –3) (2, –3) (2, –13)

Respuesta :

Hrishii

Step-by-step explanation:

[tex]y = \frac{1}{2} x - 4...(1) \\ \\ y = - 2x - 9...(2) \\ \\ from \: equations \: (1) \: and \: (2) \\ \\ \frac{1}{2} x - 4 = - 2x - 9 \\ \\ \therefore \: \frac{1}{2} x + 2x = 4 - 9 \\ \\ \therefore \: \frac{1}{2} x + 2x = - 5 \\ multiplying \: throughout \: by \: 2 \: \\ we \: find: \\ x + 4x = - 10 \\ \\ \therefore \: 5x = - 10 \\ \\ \therefore \: x = \frac{ - 10}{5} \\ \\ \huge \red{ \boxed{\therefore \: x = - 2}} \\ substituting \: x = - 2 \: in \: equation \: (1) \\ we \: find : \\ y = \frac{1}{2} \times (-2) - 4 \\ \therefore \:y =- 1 - 4 \\ \\ \huge \purple{ \boxed{\therefore \:y = - 5}} \\ \\ \pink { \boxed{\therefore \: \{x, \: \: y \} = \{ - 2, \: \: - 5 \}}} \: \\ is \: the \: solution \: set.[/tex]

Answer: (–2, –5)

Step-by-step explanation:

The given system of linear equations is expressed as

y = 1/2x - 4 - - - - - - - - - - - - -1

y = -2x - 9- - - - - - - - - - - - - -2

We would apply the method of substitution by equating equation 1 to equation 2, it becomes

1/2x - 4 = -2x - 9

Adding 2x and 4 to the left hand side and the right hand side of the equation, it becomes

x/2 + 2x - 4 + 4 = -2x + 2x - 9 + 4

5x/2 = - 5

Multiplying the left hand side and the right hand side of the equation by 2, it becomes

5x/2 × 2 = - 5 × 2

5x = - 10

Dividing the left hand side and the right hand side of the equation by 5, it becomes

5x/5 = - 10/5

x = - 2

Substituting x = - 2 into equation 2, it becomes

y = -2 × - 2 - 9

y = 4 - 9

y = - 5

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