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A system of equations is shown below: x + y = 3 2x − y = 6 the x-coordinate of the solution to this system of equations is _____

Norma-Jean [14]

Answer:

The x-coordinate of the solution to this system of equations is 3

Step-by-step explanation:

Given the system of equations:

$x+y = 3$ ....[1]

$2x-y = 6$ ....[2]

Add equation [1] and [2] we have;

$x+y+2x-y = 9$

Simplify:

$3x = 9$

Divide both sides by 3 we have;

x = 3

Substitute in [1] we have;

3+y = 3

⇒y = 0

Solution for the given system of equation is= (3, 0)

Therefore, the x-coordinate of the solution to this system of equations is 3

5 0

3 years ago

Fully condense the expression. Assume that all variables represent positive numbers. (log x -2 log y+ 3 log z) (10 points)

AfilCa [17]

Answer: The required condensed expression is $\log\dfrac{xz^3}{y^2}.$

Step-by-step explanation: We are given to fully condense the following logarithmic expression assuming that all variables represent positive numbers :

$E=\log x-2\log y+3\log z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following properties of logarithms :

$(i)~\log a^b=b\log a,\\\\(ii)~\log a+\log b=\log(ab),\\\\(iii)~\log a-\log b=\log\dfrac{a}{b}.$

Therefore, from expression (i), we get

$E\\\\=\log x-2\log y+3\log z\\\\=\log x-\log y^2+\log z^3\\\\=\log(xz^3)-\log y^2\\\\=\log\dfrac{xz^3}{y^2}.$

Thus, the required condensed expression is $\log\dfrac{xz^3}{y^2}.$

5 0

3 years ago

Match the scenarios to their corresponding boundaries.

In-s [12.5K]

The correct choices based on the integers are: 1a, 2b, 3d, and 4c.

In the question, we are asked to match the scenarios to their corresponding boundaries.

miles traveled by a car in one hour: this can be non-negative numbers as the distance traveled by a car cannot be negative, but it is not infinitely possible, making the right option a. numbers between 0 and 70.
average Celsius temperature in Antarctica: is mostly negative, and even if positive, very low. making the right option b. numbers between -100 and 20.
amount of money owed on a car: this can be any non negative number without limit, making the right option d. no negative numbers.
age when a baby takes their first step: as its an age it wont be a negative number, and its a baby age so it will be very small, making the right option, c. no negative numbers and positive numbers less that 2.

Thus, the correct choices based on the integers are: 1a, 2b, 3d, and 4c.

Learn more about integers at

brainly.com/question/12399107

#SPJ1

8 0

2 years ago

15=5-(c+7) solve the equation

sergij07 [2.7K]

The variable c is equal to 13

3 0

3 years ago

What is the range of this relation?

VARVARA [1.3K]

Answer:

Domain = {-5,2,4,6,8,9), range = (-3,-1,0,4,6,7}

Step-by-step explanation:

{(2,4), (8,-3), (-5,-1), (4,6), (6,7), (9,0)}

The domain is the input and the range is the output

domain is { 2,8,-5,4,6,9} and the range is {4,-3,-1,6,7,0}

We put the numbers in order from smallest to largest

Domain = {-5,2,4,6,8,9), range = (-3,-1,0,4,6,7}

5 0

3 years ago

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Please help if you want brianleits pleaee :( ni links please​

Please help if you want brianleits pleaee :( ni links please