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3 years ago

Solve the following system of equations using the substitution method 5x+3y=1 X+2y=3

Mathematics

2 answers:

DedPeter [7]3 years ago

4 0

Answer:

(x, y) = (-1, 2)

Step-by-step explanation:

Substitution is easier if you already have an expression for the variable you want to make a substitution for. Here, we don't have that, but we have an equation with x having a coefficient of 1. We can use that to write an expression for x:

x = 3 -2y . . . . . subtract 2y from both sides of the second equation

5(3 -2y) +3y = 1 . . . . substitute for x in the first equation

15 -10y +3y = 1 . . . . . eliminate parentheses

-7y = -14 . . . . . . . . . . subtract 15, collect terms

y = 2 . . . . . . . . . . . . . divide by -7

Use this value in the equation for x:

x = 3 -2(2) = -1

The solution is (x, y) = (-1, 2).

max2010maxim [7]3 years ago

3 0

Answer:

x= -1

y= 2

Step-by-step explanation:

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The splitting apart of one cell to form two new cells is called

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The answer is A) Mitosis

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3 years ago

A recent study claims that business travelers spend an average of $39 per day for meals. A sample of 15 business travelers found

4vir4ik [10]

Answer:

The test statistic value 't' = 3.074

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 15

mean of the Population 'μ' = $39

mean of the sample x⁻ = $42

standard deviation of the sample 's' = $3.78

Degrees of freedom ν = n-1 = 15-1 =14

$t_{\frac{\alpha }{2} } = 1.769$

Null hypothesis : There is no significance difference between the means

H₀ : x⁻ = 'μ'

Alternative hypothesis : There is significance difference between the means

H₀ : x⁻ ≠ 'μ'

Test statistic

$t = \frac{x^{-} -mean}{\frac{s}{\sqrt{n} } }$

$t = \frac{42 -39}{\frac{3.78}{\sqrt{15} } }$

t = 3.074

The test value of t-statistic t = 3.074

The calculated value t = 3.074 > 1.769 at 0.05 level of significance

null hypothesis is rejected

Alternative hypothesis is accepted

Final answer:-

There is significance difference between the means

4 0

3 years ago

What is the solution to the following equation? 5(2x –6) + 20 = 10

Igoryamba

Answer:

Step-by-step explanation:

Simplifying

5(2x + -6) + 20 = 10

Reorder the terms:

5(-6 + 2x) + 20 = 10

(-6 * 5 + 2x * 5) + 20 = 10

(-30 + 10x) + 20 = 10

Reorder the terms:

-30 + 20 + 10x = 10

Combine like terms: -30 + 20 = -10

-10 + 10x = 10

Solving

-10 + 10x = 10

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.

-10 + 10 + 10x = 10 + 10

Combine like terms: -10 + 10 = 0

0 + 10x = 10 + 10

10x = 10 + 10

Combine like terms: 10 + 10 = 20

10x = 20

Divide each side by '10'.

x = 2

Simplifying

x = 2

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3 years ago

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Answer:

Step-by-step explanation:

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