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2 years ago

X=y+2 X=2y+1 Solving Systems of Equations by subtraction Please solve this

Mathematics

1 answer:

vivado [14]2 years ago

8 0

Answer:

$x=3$

$y=1$

Step-by-step explanation:

We can subtract the first equation from the second to find the value of $y$ , although we can also do this vice versa.

$x-x=2y+1-y-2$

$y-1=0$

$y=1$

Now, we can use substitution to solve for $x$ :

$x = y+2$ (pick any equation for substitution)

$x=1+2$

$x=3$

Hope this helps :)

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he owner of a local supermarket wants to estimate the difference between the average number of gallons of milk sold per day on w

stellarik [79]

Answer:

90% confidence interval is ( -149.114, -62.666 )

Step-by-step explanation:

Given the data in the question;

Sample 1 Sample 2

x"₁ = 259.23 x"₂ = 365.12

s₁ = 34.713 s₂ = 48.297

n₁ = 5 n₂ = 10

With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }

significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1

Since we are to assume that variance are equal and they are know, we will use pooled variance;

Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13

Now, pooled estimate of variance will be;

$S_p^2$ = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]

we substitute

$S_p^2$ = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]

$S_p^2$ = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [ 4 + 9 ]

$S_p^2$ = [ 4819.9692 + 20993.4 ] / [ 13 ]

$S_p^2$ = 25813.3692 / 13

$S_p^2$ = 1985.64378

Now the Standard Error will be;

$S_{x1-x2$ = √[ ( $S_p^2$ / n₁ ) + ( $S_p^2$ / n₂ ) ]

we substitute

$S_{x1-x2$ = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]

$S_{x1-x2$ = √[ 397.128756 + 198.564378 ]

$S_{x1-x2$ = √595.693134

$S_{x1-x2$ = 24.4068

Critical Value = $t_{\frac{\alpha }{2}, df$ = $t_{0.05, df=13$ = 1.771 { t-table }

So,

Margin of Error E = $t_{\frac{\alpha }{2}, df$ × [ ( $S_p^2$ / n₁ ) + ( $S_p^2$ / n₂ ) ]

we substitute

Margin of Error E = 1.771 × 24.4068

Margin of Error E = 43.224

Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89

So, Limits of 90% CI will be; x₁ - x₂ ± E

Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114

Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666

Therefore, 90% confidence interval is ( -149.114, -62.666 )

3 0

3 years ago

If the product of two integers is positive, their signs are positive or negative

worty [1.4K]

Answer:

It could be both 2 positives, or 2 negatives.

Step-by-step explanation:

This is because a negative times a negative is a positive, and a positive times a positive is a positive.

7 0

3 years ago

Which statement is true regarding triangle TU?

blsea [12.9K]

Answer:

angle v is the smallest

Step-by-step explanation:

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3 years ago

What is 4x plus 6 plus 3 equals seventeen

Allushta [10]

The answer is 3.

the equation: 4x+6+3=17
4x+9=17
subtract 9 from both sides
4x=12
x=3

check by inserting 3 as x into the original equation

4*3+6+3=17

hope this helps!

7 0

3 years ago

A system of equations is graphed on the coordinate plane. y=−6x−3y=−x+2 What is the solution to the system of equations? Enter t

Mamont248 [21]

If you equate both, the y is eliminated:

-6x-3 = -x+2

Simplify this to find x:

-5x = 5
x = -1

Fill in x=-1 in either equation:

y = --1 + 2 = 3

So (-1,3) is the solution, it is where the lines intercept.

6 0

2 years ago

Read 2 more answers