Mathematics College

use the linear combination method to solve the system of equations. Explain each step of your solution. 2x-3y=13 x+2y=-4

Answers

Answer 1

Answer:

Solution: x = 2, y = -3.

Step-by-step explanation:

Given system of equations:

Equation 1: 2x - 3y = 13

Equation 2: x + 2y = -4

Multiply Equation 2 by 2:

2(x + 2y) = 2(-4)

Simplified: 2x + 4y = -8

Add Equation 1 and Equation 3:

4x + y = 5

Solve Equation 4 for y:

y = 5 - 4x

Substitute y into Equation 2:

x + 2(5 - 4x) = -4

Simplify:

-7x + 10 = -4

Solve for x:

x = 2

Substitute x into Equation 5:

y = 5 - 4(2)

y = -3

Solution: x = 2, y = -3.

Related Questions

please help fast i don’t feel like typing

Answers

Answer:

he should have subtracted 17 from both sides of the equation

Step-by-step explanation:

x+ 17 = 22

subtract 17 from both sides

X + 17 = 22

-17 -17

x = 5

i need the answer for this asap Please!

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The system of inequalities for the graph is

a) y < 3x - 4

b) y = x + 3

Given data ,

Let the inequality equations be represented as A and B

where

Let the first point be P ( 0 , 3 )

Let the second point be Q ( -3 , 0 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 3 - 0 ) / ( 0 + 3 )

m = 1

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 0 = 1 ( x + 3 )

y = x + 3

And , the second equation is

Let the first point be R ( 0 , -4 )

Let the second point be S ( 2 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( -4 - 2 ) / ( 0 - 2 )

m = -6/-2

m = 3

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 2 = 3 ( x - 2 )

Adding 2 on both sides , we get

y = 3x - 4

Since , it is a dotted line ,

y < 3x - 4

And , the solution to the inequality is point of intersection

where A ( 3.5 , 6.5 ) is the solution

Hence , the inequality equations are solved and A ( 3.5 , 6.5 ) is the solution

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The graph represents a relation where x represents the independent variable and y represents the dependent variable.

A coordinate plane with points at negative 4 comma 4, negative 2 comma 0, 0 comma negative 3, 3 comma 1, and 5 comma negative 2.

What is the domain of the relation?

{−4, −3, −2, 0, 1, 3, 4, 5}
{−4, −2, 0, 3, 5}
{−3, −2, 0, 1, 4}
{0, 3, 4, 5}

Answers

The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.

How to determine domain relation?

The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.

Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.

Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.

Hence, the correct option is {−4, −2, 0, 3, 5}.

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Roughly how much more does auto insurance cost for a 16 year old compared to a middle aged (40-50 year old) driver

Answers

A 16-year-old on their own policy pays on average $4,000 more per year than a 50-year-old would have to pay

The cost of insurance

Auto insurance costs vary significantly depending on factors such as location, vehicle type, and driving history. However, on average, a 16-year-old driver can expect to pay significantly more for auto insurance compared to a middle-aged driver (40-50 years old).

The exact amount varies, but it's not uncommon for a 16-year-old driver to pay two to three times more for auto insurance than a middle-aged driver. This is mainly because younger drivers are considered riskier due to their inexperience and higher likelihood of being involved in accidents.

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if gender would not have mattered, what would have been the number of males that would have survived, given the data for the number of females who survived (296/402) and the total number of passengers on the ship (1207).

Answers

If gender did not matter then the number of males who would have survived would be 593 males

How to find the number who would have survived ?

If gender would not have mattered, the survival rate would be the same for both genders. So, we would use the survival rate of females (which is 296/402) to calculate the expected number of males that would have survived.

First, calculate the survival rate of the females:

Survival rate = Number of females who survived / Total number of females

= 296 / 402

= 0.737

Expected number of male survivors = Number of males * Female survival rate

= 805 x 0.737

= 593 males

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Find the 15th term of the geometric sequence 2,6,18,...

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Answer:

In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio (r).

In this case, the first term (a₁) is 2, and the common ratio (r) can be found by dividing any term by its preceding term. Let's calculate it:

r = 6 / 2 = 3

Now, to find the 15th term (a₅₊₁₋₅), we can use the formula:

aₙ = a₁ * r^(n-1)

Substituting the values, we have:

a₁ = 2

r = 3

n = 15

a₁₅ = 2 * 3^(15-1)

Calculating the exponent first:

3^(15-1) = 3^14 = 4782969

Now, substituting this value back into the formula:

a₁₅ = 2 * 4782969

a₁₅ = 9565938

Therefore, the 15th term of the geometric sequence 2, 6, 18, ... is 9565938.

Step-by-step explanation:

Help My Daughter we not understanding?

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Representation of a number in three different ways:

133: [12 tens and 13 ones], [13 tens and 3 ones], [1 hundred, 3 tens and 3 ones]

678: [67 tens and 8 ones], [60 tens and 78 ones], [6 hundreds, 7 tens and 8 ones]

877: [80 tens and 77 ones], [87 tens and 7 ones], [8 hundred, 7 tens and 7 ones]

543: [54 tens and 3 ones], [50 tens and 43 ones], [5 hundreds, 4 tens and 3 ones]

453: [45 tens and 3 ones], [40 tens and 53 ones], [4 hundreds, 5 tens and 3 ones]

341: [30 tens and 41 ones], [34 tens and one], [3 hundreds,4 tens and one]

555: [50 tens and 55 ones], [55 tens and 5 ones], [5 hundreds, 5 tens and 5 ones]

485: [48 tens and 5 ones], [40 tens and 85 ones], [4 hundreds, 8 tens and 5 ones]

789: [78 tens and 9 ones], [70 tens and 89 ones], [7hundreds, 8 tens and 9 ones]

864: [86 tens and 4 ones], [80 tens and 64 ones], [8 hundreds, 6 tens and 4 ones]

652: [65 tens and 2 ones], [60 tens and 52 ones], [6hundreds, 5 tens and 2 ones]

Here given an example to write a particular number in different representations.

13 tens and 12 ones = 13*10 + 12*1 = 130 + 12 = 142.

14 tens and 2 ones = 14*10 + 2*1 = 140 + 2 = 142.

1 hundred, 4 tens and 2 ones = 1*100 + 4*10 + 2*1 = 100 + 40 + 2 = 142.

So three representations are of number 142.

Rest blanks should be filled in same manner taking different numbers for each rows and three columns of each row should be filled with three different representation of that assumed numbers.

Representations for some numbers: