Rowen7idn
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The diagram shows two straight lines. Both lines intersect at point A. У y = 4x A х A y = -2 Identify the coordinates of point A. (3-2) (-2,-5) , -8 (-2,2) () (2-2 ) A B D​

The Diagram Shows Two Straight Lines Both Lines Intersect At Point A У Y 4x A Х A Y 2 Identify The Coordinates Of Point A 32 25 8 22 22 A B D class=

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Jacob193idn

Answer:

Point [tex]A[/tex] is at [tex](-1/2,\, -2)[/tex].

Step-by-step explanation:

The intersection [tex](x,\, y)[/tex] of two lines in a plane could be found by solving a linear system of two unknowns ([tex]x[/tex] and [tex]y[/tex]) and two equations (one for each line.)

In this question, the equation of the two lines are [tex]y = 4\, x[/tex] and [tex]y = -2[/tex], respectively. The corresponding system of equations would be:

[tex]\left\lbrace \begin{aligned} & y = 4\, x \\ & y = -2\end{aligned} \right.[/tex].

Solve this system for [tex]x[/tex] and [tex]y[/tex]:

  • [tex]y = (-2)[/tex].
  • Substitute [tex]y = (-2)[/tex] into the first equation and solve for [tex]x\![/tex]: [tex]x = (-1/2)[/tex].

Therefore:

[tex]\left\lbrace \begin{aligned} & x = -\frac{1}{2} \\ & y = -2\end{aligned} \right.[/tex].

Thus, the coordinates of this intersection [tex](x,\, y)[/tex] would be [tex](-1/2,\, -2)[/tex].

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