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Softa [21]
3 years ago
5

Graph the system. Tell whether the system has one solution, no solution, or infinitely many solutions. y = –2x + 1 y = –2x – 3

Mathematics
1 answer:
Alchen [17]3 years ago
8 0
Let's try the actual solution of the system

<span>y = –2x + 1
y = –2x – 3

Note that the slopes of the graphs of these two lines are the same:  -2.

That means that the lines are parallel to one another.

Only the y-intercepts (1 and -3) are different.

Since the 2 lines never intersect, the system has no solution.

</span>
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Y = 2/3 x -3 y = -3/2 x +2 what statement about the lines are true
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Answer:

The product of the slopes of lines is -1.

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Thus, the lines are perpendicular.

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given the lines

y = 2/3 x -3       --- Line 1

y = -3/2x +2      --- Line 2

<u>The slope of line 1</u>

y = 2/3 x -3       --- Line 1

By comparing with the slope-intercept form of the line equation

The slope of line 1 is: m₁ = 2/3

<u>The slope of line 2</u>

y = -3/2x +2      --- Line 2

By comparing with the slope-intercept y = mx+b form of the line equation

The slope of line 2 is: m₂ = -3/2

We know that when two lines are perpendicular, the product of their slopes is -1.

Let us check the product of two slopes m₁ and m₂

m₁ × m₂ = (2/3)(-3/2 )

m₁ × m₂ = -1

Thus, the product of the slopes of lines is -1.

i.e. m₁ × m₂ = -1

Thus, the lines are perpendicular.

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