What is the answer to 4t+9=-8t-13

Remember, you can do anything to an euation as long as you do it to both sides

4t+9=-8t-13
add 8t to both sides
12t+9=-13
minus 9 from both sides
12t=-22
divide both sides by 12

Hi!

4t+9=-8t-13

To solve, first add 13 to both sides.
4t+9+13=-8t-13+13
4t+22=-8t
Subtract 4 from both sides
4t-4+22=-8t-4
22=-12t
Divide by -12 on both sides
22/12=-12t/-12
22/-12 = t
Which can be simplified to...
-11/6 = t

The answer is t = -11/6

Hope this helps! :)

  (a)  y = 5/2x +3

  (b)  y = -1/2x +9/2

  (c)  consistent, independent

  (d)  (0.5, 4.25)

Step-by-step explanation:

(a) The 2-point form of the equation of a line is a good place to start:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

Filling in the point values, we have ...

  y = (8 -3)/(2 -0)(x -0) +3

  y = 5/2x +3 . . . . . . simplify

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(b) Similarly, filling in the point values, we have ...

  y = (3 -4)/(3 -1)(x -1) +4

  y = -1/2(x -1) +4 . . . . . . simplify

  y = -1/2x +9/2 . . . . . . . eliminate parentheses, collect terms

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(c) The lines have different slopes, so are consistent and independent.

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(d) Substituting for y, we have ...

  5/2x + 3 = -1/2x + 9/2

  5x +6 = -x +9 . . . . . . . . . . . . multiply by 2 to eliminate fractions

  6x = 3 . . . . . . . . . . . . . . . . . . add x-6

  x = 3/6 = 1/2 . . . . . . . . . . . . . divide by the x-coefficient

Using the equation for Sidewalk 2, we can find y:

  y = -1/2(1/2) +9/2

  y = 17/4

The point of intersection is (x, y) = (1/2, 17/4).