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BabaBlast [244]
2 years ago
12

Solve the following system by graphing and identify the point of intersection -5x+2y=-4 2x-y=2

Mathematics
2 answers:
FrozenT [24]2 years ago
8 0

Answer: Point of intersection (0, -2)

Step-by-step explanation:

guajiro [1.7K]2 years ago
8 0

Answer:

S =  (0, -2)

Step-by-step explanation:

Convert both standard form equations to slope-intercept form.

-5x+2y=-4 ⇒ y = 5/2(Decimal form: 2.5)x - 2

2x-y=2 ⇒ y = 2x - 2

Given:

⇒ L1 = y = 5/2x - 2

⇒ L2 = y = 2x - 2

The intersection is point:

⇒ S = (0, -2)

Steps:

To find intersection point we need to solve the following system of equations.

  • y = 5/2x - 2
  • y = 2x-2

STEP 1: Solve for x

5/2x - 2 = 2x - 2

5/2x - 2x = -2 + 2

1/2x = 0

x = 0

STEP 2:  Solve for y by substituting x = 0 into  first equation.

y = 5/2 * 0 - 2 = 0 - 2 = -2

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now you are buying 1/2 a dollar's worth of jelly beans, so you will be getting 1/2 * 300 / x which is equal to 150 / x jelly beans.
the actual number of jelly beans you get is determined by x.
if x = 1, the you get 150 jelly beans for 1/2 of a dollar.
if x = 3, then you get 50 jelly beans for 1/2 of a dollar.

you can also work this out by determing the cost per jelly bean.
if you pay x dollars for 300 jelly beans, then the cost per jelly bean is equal to x/300.
now you want to buy 50 cents worth of jelly beans.
the number of jelly beans you can buy is the money you pay divided by the cost per jelly bean.
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another way to look at it would be to set up a ratio.
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simplify to get:
150 = x*y
divide both sides of the equation by x to get:
y = 150/x
same equation again.
x is the cost for 300 jelly beans.
y is the number of jelly beans you can get for half a dollar.
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