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Marianna [84]
3 years ago
5

10. 10x + 5y = 15 y=2x-3

Mathematics
1 answer:
Ivan3 years ago
6 0

Answer:

(i think) 1.5

Step-by-step explanation:

If you replace y with the equation y=2x-3, you get 5(2x - 3)

if you distribute this, it equals 10x - 15

combining like terms 10x + 10x - 15=15 will turn into 20x - 15 = 15

if you add 15 to both sides, -15 will cancel and 15 will turn into 30

20x = 30

divide both sides by 20 which will lead to x=1.5

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Write the equation of the line parallel to 4x-5y=2 and passing through point (0,0)
kotykmax [81]

k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\\\\k\ ||\ l\iff m_1=m_2

We have:

4x-5y=2\ \ \ \ |-4x\\\\-5y=-4x+2\ \ \ \ |:(-5)\\\\y=\dfrac{4}{5}x-\dfrac{2}{5}\to m_1=\dfrac{4}{5}\\\\l:y=m_2x+b\\\\k\ \prep\ l\Rightarrow\dfrac{4}{5}m_2=-1\ \ \ \ |\cdot\dfrac{5}{4}\\\\m_2=-\dfrac{5}{4}

l:y=-\dfrac{5}{4}x+b

The line l is passing through point (0, 0). Substitute the coordinates of the point to the equation of a line l:

0=-\dfrac{5}{4}\cdot0+b\to b=0

y=-\dfrac{5}{4}x\ \ \ \ |\cdot4\\\\4y=-5x\ \ \ \ |+5x\\\\5x+4y=0

<h2>Answer: 5x + 4y = 0</h2>
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