Solve by the elimination method.
2x – 3y = 2
3x + 2y = 29

x=7, y=4

Step-by-step explanation:

2x – 3y = 2 , this will be equation 1.

3x + 2y = 29, this will be equation 2.

We have to make a letter have the same coefficient in the two equations.

lets make x have the same coefficient in the two equations.

Multiply the whole of equation 1 by 3.

3(2x - 3y = 2)

6x - 9y = 6, this will be equation 3.

Multiply the whole of equation 2 by 2.

2(3x + 2y = 29)

6x + 4y = 58, this will be equation 4.

Now let's begin.

We'll put equation 4 up so it will be easier to solve.

6x + 4y = 58, equation 4.

6x - 9y = 6, equation 3.

Let's get rid of 6x, so we can find the value of y; we'll have to subtract equation 3 fron equation 4. Please take note of the signs, (+) and (-).

(6x-6x) + (4y-(-9y)) = (58-6)

Notice the sign change.

0 + (4y + 9y) = 52

13y = 52

Divide both sides by 13.

13y/13 = 52/13

y = 4

To find x, we'll have to substitute y into equation 1 or equation 2. Let's use both.

EQUATION 1

2x – 3y = 2

2x - 3(4) = 2

2x - 12 = 2

Add 12 to both sides.

2x - 12 (+12) = 2 (+12)

2x - 0 = 14

2x = 14

Divide both sides by 2.

2x/2 = 14/2

x = 7

EQUATION 2

3x + 2y = 29

3x + 2(4) = 29

3x + 8 = 29

Subtract 8 from both sides.

3x + 8 (-8) = 29 (-8)

3x + 0 = 21

3x = 21

Divide both sides by 3.

3x/3 = 21/3

x = 7

Therefore, the answers are x=7, and y=4.

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See the graph attached.

Explanation:

The repetitive up and down motion of a weight (mass) in a spring depicts the simple harmonic motion.

The most basic equation for the simple harmonic motion around the rest position is:

           

Where A is the amplitude, T is the period, and t is the time.

The amplitude A is the vertical distance between the crest of the wave and the equilibrium (rest) position. It is half the maximum displacement of the mass.

The maximum displacement is the difference between the lowest and the highest points, which is 20 inches in the problem.

Hence, A = 20 / 2 = 10

The period, T, is the time for a complete cycle. This is the time for the weight to, starting from its resting position, reach its highest position, fall to its lowest position, and return to its resting position. This time is 8 seconds in the problem: T = 8.

Then you must graph the function:

         

Some points of that function that will permit you to draw the graph are when t = 0, t = 2, t = 4, t = 6, and t = 8

t = 0 ⇒ displacement = 10 sin(0) = 0 ⇒ (0, 0) - - - on the middle linet = 2 ⇒ displacement = 10 sin(π/2) = 10 ⇒ (2, 10) - - - maximumt = 4 ⇒ displacement = 10 sin(π) = 0 ⇒ (4, 0) t = 6 ⇒ displacement = 10 sin(3π/2) = 10 ⇒ (6, - 10) - - - minimumt = 8 ⇒ displacement = 10 sin(4π) = 10 ⇒ (8, -0)

With that, you can sketch the function. Now, find attached the drawing using a graph calculator.