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Inessa [10]
3 years ago
6

Does this equation have no solution, one solution, or infinite number of solutions x=y-3 2x-2y=-6

Mathematics
1 answer:
lianna [129]3 years ago
7 0

Answer:

Infinite amount of solutions

General Formulas and Concepts:

<u>Pre-Alg</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

<u>Alg I</u>

  • Solving systems of equations by substitution/elimination

Step-by-step explanation:

<u>Step 1: Define systems</u>

x = y - 3

2x - 2y = -6

<u>Step 2: Solve for </u><em><u>y</u></em>

  1. Substitute:                              2(y - 3) - 2y = -6
  2. Distribute 2:                            2y - 6 - 2y = -6
  3. Combine like terms:              -6 = -6

Here we see that -6 does equal -6. Therefore, any value <em>y</em> would work as a solution. Hence, this systems of equations has an infinite amount of solutions.

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This week, we are covering relationships that can be approximated by linear equations. For instance, y = 453x + 3768 represents
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Answer:

See explanation below.

Step-by-step explanation:

We assume that the data is given by :

x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90

y: 38, 43, 29, 32, 26, 33, 19, 27, 23, 14, 19, 21.

Where X represent the cost for scholarships in thousands of dollars and y represent the cost of life for an academic semester (The data comes from the web)

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For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i = 30+30+30+50+50+50+70+70+70+90+90+90=720

\sum_{i=1}^n y_i =38+43+29+32+26+33+19+27+23+14+19+21=324

\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200

\sum_{i=1}^n y^2_i =38^2+43^2+29^2+32^2+26^2+33^2+19^2+27^2+23^2+14^2+19^2+21^2=9540

\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=49200-\frac{720^2}{12}=6000

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=17540-\frac{720*324}{12}{12}=-1900

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m=-\frac{1900}{6000}=-0.317

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\bar x= \frac{\sum x_i}{n}=\frac{720}{12}=60

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And we can find the intercept using this:

b=\bar y -m \bar x=27-(-0.317*60)=46.02

So the line would be given by:

y=-0.317 x +46.02

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