Answer :
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 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
[tex]\frac{1.5}{1.6}\neq \frac{0.2}{0.3}\neq \frac{2.68}{2.98}[/tex]
⇒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).