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MArishka [77]
3 years ago
10

Solve the system of equations, y = x – 3 and y = –2x + 6, using the substitution method.

Mathematics
2 answers:
kvasek [131]3 years ago
7 0

Answer:

x=9

Step-by-step explanation:

-2x+6=x-3

-1x+6=-3

-1x=-9

divide both sides by -1

x=9

hope this helps

Yuri [45]3 years ago
7 0

Answer:

  • (3, 0)

Step-by-step explanation:

<u>Given system:</u>

  • y = x – 3 and
  • y = –2x + 6

<u>Substitute y and solve for x:</u>

  • x - 3 = -2x + 6
  • x + 2x = 6 + 3
  • 3x = 9
  • x = 3

<u>Find y:</u>

  • y = x - 3 = 3 - 3 = 0

<u>Solution is:</u>

  • (3, 0)
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To get the shortest distance from a point to a line, we need to find a perpendicular line that intersects the line and also intersects the line. We know the slope of the line will be 1/2, but to find the y-intercept, we can just plug it into the point because we already know it will be on the line.

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Now, we know the slope and the y-intercept, and since it will intersect the other line, we can set it equal to the other lines formula:

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Plugging into distance formula:

\sqrt{(-2 - \frac{16}{5})^2+(-3-(-\frac{2}{5}))^2}\\=  \sqrt{(-5.2)^2+(-2.6)^2}\\= \sqrt{33.8}

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