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7nadin3 [17]
2 years ago
8

Hey can someone tell me the steps to solving a system of equations with graphing

Mathematics
1 answer:
ryzh [129]2 years ago
4 0

Answer:

Let's go through the following example to show how to solve a system of equations by graphing. I won't solve this system, I will just show how to.

8x-3y = 17\\4x+y=21

<h3>If you can use an online graphing calculator...</h3>

If you have an online grapher (like Desmos) at your disposal, then you can put each equation in it as it is.

  • Lines intersect -> Put your cursor over the point of intersection to get the solution.
  • Lines never intersect -> The lines are parallel and there is no solution
  • Lines perfectly fall on each other -> The lines are the same and have infinite solutions

<h3>If you have a physical graphing calculator (like TI-84)</h3>

1. Get both equations in the form y=mx+b by solving for y.

8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{17}{3}               4x+y=21\\y=-4x+21

2. Put both equations in the graphing calculator

  • Lines intersect -> Find the intersection point using your graphing calculator's mechanics (each one is a little different)
  • Lines never intersect -> The lines are parallel and there is no solution
  • Lines perfectly fall on each other -> The lines have the same equation and have infinite solutions

<h3>If you just have graphing paper...</h3>

1. Get both equations into the form y=mx+b by solving for y.

8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{17}{3}                    4x+y=21\\y=-4x+21

2. Plug in a few different points for x and calculate their y-values.

3. Plot those points on the graph paper

  • Lines intersect -> Find the intersection point's coordinates to get the solution for x and y.
  • Lines never intersect -> The lines are parallel and there is no solution
  • Lines perfectly fall on each other -> The lines have the same equation and have infinite solutions.
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The base of a pentagonal prism is regular with an apothem of 4 cm. The height of the prism is 16 cm. Find the volume of the pris
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Answer:

volume ≈ 930 cm³ (nearest cubic cm)

Step-by-step explanation:

The base of the prism which is a pentagon is regular. The apothem which is a line drawn from the center to any side of the pentagon is 4 cm. The height of the prism is 16 cm.

The volume of a prism = Bh

where

B = base area

h = height of the prism

The base of the prism can be divided into 5 congruent triangles.But the base of the triangles is unknown.

The sum of interior angle of a pentagon is 540°. That means each angle is 108° . The triangle divide the angle into 2. Making the 2 base angle as 54° each. The last angle of the triangle at the center is 72°(remember sum of angle in a triangle is 180° which is 54° + 54° + 72° = 180°) .

The angle form the center can be divided by the line of height of the triangles. The angle will then be 36°. Using tangential ratio half of the length of the base of the triangle can be known. Therefore,

tan 36° = opposite/adjacent

tan 36° = opposite/4

opposite = 4 tan 36°

The full base of the triangles = 2(4 tan 36°)

area of each triangle = 1/2 × 2(4 tan 36°) × 4 = 16 tan 36°

Base area of the prism(pentagon) = 5 × 16 tan 36° = 80 tan 36°

Volume of the prism = Bh

where

h = 16 cm

B = 80 tan 36°

volume =  80 tan 36° × 16 = 1280  tan 36° = 1280  × 0.726542528

volume = 929.974435847  cm³

volume ≈ 930 cm³ (nearest cubic cm)

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Area of triangle=1/2 times base times  height
given that area=24 and height=6
24=1/2 times base times 6
24=1/2 times 6 times base
24=3 times base
divide both sides by 3
8=base
the base is 8 units long
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