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Represent the system of linear equations 3x+y-5=0 and 2x-y-5=0 graphically. From the graph write solution of the system and also the area of the triangle formed by the lines and y axis

Respuesta :

Answer:

The solution is (2, -1)

The area of the triangle formed is 10 square units.

Step-by-step explanation:

The given system is

[tex]3x+y-5=0\\2x-y-5=0[/tex]

First, you need to graph both lines. To do so, you just need to find the interceptions with both axis.

[tex]3x+y-5=0[/tex]

For [tex]x=0 \implies y=5[/tex]

For [tex]y=0 \implies x=\frac{5}{3}[/tex]

Then, you draw both points to have the straight line.

Repeat the process for the second line. The image attached shows both lines.

Remember, the solution of a linear system of equation is the common point between lines. In this case, we can observe that the solution is (2, -1).

On the other hand, to find the area of the triangle formed, we need to use the length of its base and its height.

  • Its base is 10 units long.
  • Its height is 2 units long.

Now, we use the area formula for triangles

[tex]A=\frac{bh}{2}=\frac{10(2)}{2}= 10 \ u^{2}[/tex]

Therefore, the area of the triangle formed is 10 square units.

Ver imagen jajumonac

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