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4 years ago

Can someone help me with this 2x+4y+3z=6 x-2y+z=-5 -x-3y-2z=-7 solve for x,y,z

Mathematics

1 answer:

Flauer [41]4 years ago

3 0

Answer:

x = -7 2/3, y = 1 1/3 and z = 5 1/3.

Step-by-step explanation:

2x+4y+3z=6 ..... 1

x-2y+z=-5 ...... 2

-x-3y-2z=-7 .......3

Add equations 2 and 3 to eliminate x:

-5y - z = -12 .....4

Multiply equation 2 by - 2:

-2x + 4y - 2z = 10

Add this to equation 1:

8y + z = 16 ........ 5

Now add equation 4 to equation 5:

3y = 4

y = 4/3 = 1 1/3.

Now find z by substituting for y in equation 4:

-5(4/3) - z = -12

z = 12 - 20/3

z = 36/3 - 20/3 = 16/3 = 5 1/3.

Finally, we find x by substituting for y and z in equation 1:

2x + 4*4/3 + 3*16/3 = 6

2x = 6 - 16/3 - 16

2x = 18/3 - 16/3 - 48/3 = -46/3

x = 23/3 = 7 2/3.

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Answer:

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Step-by-step explanation:

Hi there!

We're given the line 5x+4y=24 and we want to find the line parallel to it that passes through (8,-5)

Parallel lines have the same slopes

First, we need to find the slope of 5x+4y=24.

We'll do that by converting 5x+4y=24 from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b where m is the slope and b is the y intercept)

subtract 5x from both sides

4y=-5x+24

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since -5/4 is in the place where m should be, it is the slope.

So the equation of the line parallel to it will also have -5/4 as the slope

Here's the equation so far in slope-intercept form:

y=-5/4x+b

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because the equation will pass through (8,-5), we can use it to solve for b

substitute 8 as x and -5 as y

-5=-5/4(8)+b

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5=b

substitute 5 as b into the equation

That's the equation of the line parallel to 5x+4y=24.

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