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

The lines intersect at (1.6,1.4).

Explanation:

1.5x + 0.2y = 2.68

0.2y = -1.5x + 2.68

y=( -1.5x + 2.68)/0.2

y=-7.5x+13.4

1.6x + 0.3y = 2.98

0.3y = -1.6x + 2.98

y=( -1.6x + 2.98)/0.3

y=-5.3333x+9.9333

The lines are not parallel because they have different slopes -7.5≠-5.3333

The lines do not overlap at all points. example for x=0 9.9333≠13.4

to get the intersection point

-5.3333x+9.9333=-7.5x+13.4

2.1667x=3.4667

x=1.6

replacing x in any of the equations

y=-7.5x1.6+13.4=1.4

Then the lines intersect at (1.6,1.4).

Answer 2

1.5x + 0.2y = 2.68....multiply by 0.3
1.6x + 0.3y = 2.98...multiply by - 0.2
------------------------
0.45x + 0.06y = 0.804 (result of multiplying by 0.3)
- 0.32x - 0.06y = - 0.596 (result of multiplying by - 0.2)
----------------------add
0.13x = 0.208
x = 0.208/0.13
x = 1.6

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
0.2y = 0.28
y = 0.28/0.2
y = 1.4

solution (they intersect at) (1.6,1.4)