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3 years ago

3x – 4y> -6 2x + y<7 y>-3

Mathematics

1 answer:

Sloan [31]3 years ago

8 0

For the 1st problem, solve the 2nd equation for x.

x = -1 - y

Now, replace x in the 1st equation with (-1 - y)

2(-1 - y) - 3y = 2

-2 - 2y - 3y = 2

-2 - 5y = 2

-5y = 4

y = -4/5

x = -1 - (-4/5) = -1 + (4/5) = -1/5

The solution is (-1/5, -4/5)

For the 2nd problem, multiply the top equation by 15 and the bottom equation by -12. That gives us:

10x - 12y = 15

-36x +12y = 84

Add the two together, which gives us:

-26x = 99

x = -99/26

Now, put this value of x into either equation to solve for y

3(-99/26) - y = -7

-297/26 - y = -7

-y = -7 + 297/26

-y = 115/26

y = -115/26

The solution to this system is (-99/26, -115/26)

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3 years ago

The point-slope form of the equation of the line that passes through (-4,-3) and (12, 1) is y-1= 1/4(x-12). what is the stadard

Monica [59]

Answer:

x - 4y = 8

Step-by-step explanation:

Since the Point-Slope Formula is already given to you, convert it to Slope-Intercept Form, and you do that by doing this:

y - 1 = ¼(x - 12) >> y - 1 = ¼x - 3

y - 1 = ¼x - 3

+ 1 + 1

--------------

y = ¼x - 2 >> Slope-Intercept Form

After doing this, you are ready to convert to Standard Form, and you do that by doing this:

y = ¼x - 2

-¼x -¼x

-----------

-¼x + y = -2

Now unfortunately, we do not want fractions as our coefficients, so the way to eliminate the fraction is to multiply the equation by the Multiplicative Inverse of -¼, which is -4:

-4[-¼x + y = -2] >> x - 4y = 8 → New equation without fractions

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