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bonufazy [111]
3 years ago
10

use the elimination method to solve the system of equations. choose the correct ordered pair. 7x+3y=30 -2x+3y=3

Mathematics
1 answer:
andreev551 [17]3 years ago
3 0

Answer:

x = 3, y = 3

Step-by-step explanation:

Elimination method to find x:

  (7x + 3y = 30) * -1      ===>                              -7x - 3y = -30

                                                                          -2x + 3y = 3                    

  add two equations to eliminate y             ______________

                                                                                 -9x = -27     ===>   x = 3

substitution to find y:  

  -2x + 3y = 3

  -2(3) + 3y = 3

  -6 + 3y = 3

  3y = 9

    y = 3

Elimination method to find y:

  (7x + 3y = 30) * 2         ===>                           14x + 6y = 60

  (-2x + 3y = 3)  * 7         ===>                         -14x + 21y = 21

  add two equations to eliminate x             ______________

                                                                              27y = 81      ===>   y = 3

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son4ous [18]

Answer:

y=\frac{5}{4}x+\frac{15}{4}

Step-by-step explanation:

x | y

-------

1     5

5   10

9    15

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This one is linear because as x goes up by the same number so does y. So the ratio of difference of y to difference of x is the same per pair of points.

So a linear equation in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

To find the slope, I'm going to line up the points vertically and subtract, then put 2nd difference over 1st difference. Like so,

( 1    ,   5)

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

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So the slope is 5/4 which makes sense since the y's are going up by 5 each time and the x's are going up by 4 each time.

So we have m=5/4. Let's plug that into our y=mx+b.

y=5/4 x+b

To find b, we need to use y=5/4 x+b along with one of the given points.

Choose; it doesn't matter.  I like (1,5) I guess.

y=5/4 x +b with (1,5)

5=5/4 (1)+b

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15/4=b

The y-intercept is 15/4 so b=15/4.

So the equation for the line in slope-intercept form is y=5/4 x +15/4.

y=\frac{5}{4}x+\frac{15}{4}

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