Question

Which statement describes the graph of the system of equations below? 1.5x + 0.2y = 2.68 1.6x + 0.3y = 2.98 The lines are parallel. The lines overlap at all points. The lines intersect at (1.6,1.4). The lines intersect at (3.1,0.5).

Answer 1

Here we are given two equations:

$1.5x + 0.2y = 2.68$

$1.6x + 0.3y = 2.98$

Now let us try to graph them so that we can find the answer.

Using table method to graph.

$1.5x + 0.2y = 2.68$

Let us say x=0,

0+0.2y=2.68

y=13.4

first point is (0,13.4)

let us say y=0,

1.5x +0=2.68

x=1.79

second point is (1.79,0)

So two point for first equation are (0,13.4) and (1.79,0).

Now for second equation,

$1.6x+0.3y=2.98$

let us say x=0,

0+0.3y = 2.98

y=9.93

first point is (0,9.93)

now say y=0,

1.6x + 0 =2.98

x=1.86

second point is (1.86,0)

two points for second equation are (0.9.93) and (1.86,0)

Graph is shown in figure below.

Answer: So the two lines intersect at point (1.6,1.4).

Answer 2

Answer:

line intersect at (1.6 , 1.4)

Step-by-step explanation:

The two equations given are :

1.5x + 0.2y = 2.68

1.6x + 0.3y = 2.98

Solve this two equation :

                     0.3 ( 1.5x + 0.2y = 2.68 )  = 0.45x + 0.06y = 0.804

                     0.2  ( 1.6x + 0.3y = 2.98 ) = 0.32x + 0.06y = 0.596

                0.45x + 0.06y = 0.804

          (-)   0.32x + 0.06y = 0.596

             = 0.13x   + 0        = 0.208

                                0.13x = 0.208

                                      x = 0.208 / 0.13

                                      x =  1.6    

Put the value of x in any of the equation, we will get the value of y

                           1.5x + 0.2y = 2.68

                  (1.5 * 1.6 ) + 0.2y = 2.68

                            2.4 + 0.2y = 2.68

                                     0.2y = 2.68 - 2.4

                                          y = 0.28 / 0.2

                                          y = 1.4

Hence the intersection point is ( 1.6 , 1.4)

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