Respuesta :
Using location of points and a system of equations, it is found that:
- The value of x is 3.
- The value of y is 4.
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Point C is located between points B and D means that:
[tex]BD = BC + CD[/tex]
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We are given that:
- [tex]BC = 5x + 7[/tex]
- [tex]CD = 3y + 4[/tex]
- [tex]BD = 38[/tex]
- [tex]BD = 2x + 8y[/tex]
From this, two equations can be built.
[tex]2x + 8y = 38[/tex]
Dividing both sides by 2:
[tex]x + 4y = 19[/tex]
[tex]x = 19 - 4y[/tex]
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Finding y:
[tex]BC + CD = BD[/tex]
[tex]5x + 7 + 3y + 4 = 38[/tex]
[tex]5x + 3y + 11 = 38[/tex]
[tex]5x + 3y = 27[/tex]
Since [tex]x = 19 - 4y[/tex]
[tex]5(19 - 4y) + 3y = 27[/tex]
[tex]95 - 20y + 3y = 27[/tex]
[tex]17y = 68[/tex]
[tex]y = \frac{68}{17}[/tex]
[tex]y = 4[/tex]
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Finding x:
[tex]x = 19 - 4y = 19 - 4(4) = 19 - 16 = 3[/tex]
The value of x is 3.
The value of y is 4.
A similar problem is given at https://brainly.com/question/10956693
