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18 votes
18 votes
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).

User Andreas Pasternak
by
2.8k points

1 Answer

9 votes
9 votes

Answer:

3rd answer option (1.6, 1.4)

Explanation:

the slope of the lines is different.

to see we transform the equations to the regular slope-intercept form

y = ax + b

with "a" being the slope and "b" being the y-intercept (the y value when x = 0).

1.5x + 0.2y = 2.68

0.2y = -1.5x + 2.68

y = -1.5x/0.2 + 2.68/0.2 = -7.5x + 13.4

1.6x + 0.3y = 2.98

0.3y = -1.6x + 2.98

y = -1.6x/0.3 + 2.98/0.3 = -5.33333...x + 9.93333...

-7.5 is not -5.3333...

so, the lines are not parallel nor overlap at all points.

therefore, they intersect at a point.

(1.6, 1.4) ?

the equations must remain true when using the coordinates :

1.5×1.6 + 0.2×1.4 = 2.68

1.6×1.6 + 0.3×1.4 = 2.98

2.4 + 0.28 = 2.68

2.68 = 2.68 correct

2.56 + 0.42 = 2.98

2.98 = 2.98 correct

yes, they intersect at (1.6, 1.4).

for (3.1, 0.5) already the x coordinate is way too large.

1.5×3.1 or 1.6×3.1 are already by themselves much larger than 2.68 or 2.98.

User Petergus
by
3.0k points
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