Given the equations 2x+4/3 y=1 and y-9/13 x=9, by what factor would you multiply the first equation so that combining the two equations would eliminate x?

-9/26
9/26
1/2
-9/13

9/26

Step-by-step explanation:

To eliminate variable x  we need to make the coefficient of x same and different signs.

In the first fraction the coefficient of x is 2 and i the second fraction the coefficient of x is 9/13

To find the factor that make the coefficient same , we divide 9/13 by 2

9/13 divide by 2 is 9/26

LEts multiply 9/26 and check

9/26 times 2x becomes 9/13 x

We already have same -9/13 x in the second fraction

When we add both x  terms then it becomes 0. x will be eliminated

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.