Question

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

Answer 1

C is the only answer: The lines intersect at (1.6,1.4), because  (1.6,1.4) verifies the (x, y) of the  line 1.5x + 0.2y = 2.68 and also the line 1.6x + 0.3y = 2.98, that means both lines intersect at (1.6,1.4).
 

Answer 2

Answer with explanation:

The two equations in two variable in ,x and y , is

A→1.5 x + 0.2 y = 2.68

B→1.6 x + 0.3 y = 2.98

When , there are two equation of line in x y-plane, then there are three possibilities.

1. They will Intersect at a point.

2. The two lines are Parallel.

3. The two lines are Coincident.

For, the three Possibilities, we will find

 $\frac{1.5}{1.6}\neq \frac{0.2}{0.3}\neq \frac{2.68}{2.98}$

⇒it means the two lines will intersect.

Multiplying equation A , by 6 and Multiplying equation B, by 4 ,and then Subtracting B from A, we get

⇒9 x + 1.2 y - 6.4 x - 1.2 y=16.08 -11.92

⇒ 2.6 x=4.16

Dividing both sides by ,2.6, we get

→x=1.6

Substituting the value of , x in equation A

⇒1.5×1.6 + 0.2 y=2.68

→2.40 + 0.2 y=2.68

→0.2 y=2.68 -2.40

→0.2 y = 0.28

Dividing both sides by , 0.2, we get

y=1.4

Option C: ⇒ The lines intersect at (1.6,1.4).