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timurjin [86]
3 years ago
13

Solve the simultaneous equations: 5x - 3y = 12 2x - y = 5

Mathematics
2 answers:
yKpoI14uk [10]3 years ago
6 0

5x - 3y = 12

2x - y = 5 so y = 2x - 5

5x - 3(2x - 5) = 12

5x - 6x + 15 = 12

-x = 12 - 15

-x = -3

x =3

y = 2x - 5

y = 2(3) - 5

y = 6 - 5

y = 1

solutions (3,1)


stich3 [128]3 years ago
6 0
5x-3y=12
2x-y=5
I am going to use substitution method
2x-y=5                                          5x-3y=12                         25/2-25/2-1/2=12-25/2
2x-y+y=5+y                                   5(5/2+y/2)-3y=12                            -1/2y=-1/2
2x/2=5/2+y/2                                25/2+5y/2-3y=12                 -1/2y /-1/2=-1/2 /-1/2
x=5/2+y/2                                      25/2-1/2=12                                     y=1
 Therefore y=1
 5x-3y=12  5x-3(1)=12 5x-3=12 5x-3+3=12+3  5x =15 5x/5=15/5   x=3
Therefore x=3 and y=1
                                                      

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State the slope of the line perpendicular to the line -2x+5y=12
defon

Answer:

- 5/2

Step-by-step explanation:

Arrange this line equation into y = mx + b form   m = slope

 y = 2/5x + 12/5    

  then perpindicular line = - 1/m   = - 1/ (2/5) = - 5/2

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What is the equation for a line passing through (-2,3) and perpendicular to y= -1/2+1 ?
nata0808 [166]

Answer:

y=2x+7

Step-by-step explanation:

<u><em>The correct question is</em></u>

what is the equation for a line passing through (-2,3) and perpendicular to y= -1/2<em>x</em>+1 ?

Remember

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes are equal to -1)

The slope of the given line is m=-1/2

so

the opposite reciprocal is m=2

<em>Find the equation of the line in point slope form</em>

y-y1=m(x-x1)

we have

m=2\\point\ (-2,3)

substitute

y-3=2(x+2)

<em>Convert to slope intercept form</em>

y=mx+b

isolate the variable y

y-3=2x+4

y=2x+4+3

y=2x+7

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Find the midpoint of the segment with the following endpoints. (7,−2) and (1,−10)
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Answer:

The answer is

<h2>(4 \:  , \:  - 6)</h2>

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

<h3>M  = ( \frac{x1 + x2}{2} ,  \:  \frac{y1 + y2}{2} )</h3>

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(7,−2) and (1,−10)

The midpoint is

<h3>M = ( \frac{7 + 1}{2}   ,  \:  \frac{ - 2 - 10}{2} ) \\  = ( \frac{8}{2} , \:  -  \frac{12}{2} )</h3>

We have the final answer as

<h3>(4 \:  , \:  - 6)</h3>

Hope this helps you

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