YES I WILL GIVE BRAINLIST
Which of the following systems of equations has exactly one solution?

Question 1 options:

2x+y=10y=−2x+8

2x+4y=102(x+2y)=10

2(2x+1)=yy=2x+8

y=10−2xy=−2x+7



Which of the following systems of equations has infinitely many solutions?

Question 4 options:

2x+7x+y=6y=9x+6

y=5x+7y=2x+8

y=x+42y=2x+8

7x−y=10y=6x+8

Answer:

Question 1) Option C: 2(2x+1) = y, y = 2x + 8.

Question 4) Option C:  y = x + 4,  2y = 2x + 8

Step-by-step explanation:

The graph of perpendicular lines will show an intersection of two lines at a single point, forming 90° adjacent angles. Since perpendicular lines intersect at exactly one point, then it means that they will have one solution.  Additionally, perpendicular lines have negative reciprocal slopes for which multiplying the slopes of both lines result in a product of -1.

Lines that have the same slope and y-intercept. Therefore, they are equivalent equations that will result in an infinitely many solutions. The graph of these lines will coincide on top of each other, as if they are the same line.  The systems of linear equations that result in an infinitely many solutions are dependent and consistent. They are dependent if they have an infinite number of solutions, and consistent because they have at least one solution.

Parallel lines have the same slope.  A systems of linear equations whose graph involve parallel lines have no solution, as there is no point of intersection between those two lines.  Therefore, parallel lines have no solution, making it an inconsistent system.

We must transform these equations in its slope-intercept form, y = mx + b, which will allow us to easily determine the type of lines a given system has based on their slopes.

Equation 1:  2x + y = 10

Equation 2: y = −2x + 8

Transform Equation 1 to slope-intercept form:

2x + y = 10

Subtract 2x from both sides:

2x - 2x + y = - 2x + 10

y = -2x + 10  ⇒ This is the slope-intercept form of Equation 1.

Since Equations 1 and 2 have the same slope, but different y-intercepts, then it means that they are parallel lines that have no point of intersection.

Transform both equations to slope-intercept form:

Equation 1:  2x + 4y = 10

                   [tex]\large\bf\sf{y\:=\:-\frac{1}{2}x\:+\:\frac{5}{2}}[/tex]  ⇒ This is the slope-intercept form of Equation 1.

Equation 2:  2(x+2y) = 10

Distribute 2 into the parenthesis:

2(x+2y) = 10

2x + 4y = 10  ⇒ It is clear at this point that this equation matches Equation 1. Thus, the slope-intercept form of Equation 2 will be the same:

[tex]\large\bf\sf{y\:=\:-\frac{1}{2}x\:+\:\frac{5}{2}}[/tex]  ⇒ Slope-intercept form of Equation 2.

It turns out that Equations 1 and 2 are equivalent, as they have exactly the same slope and y-intercept. Therefore, they have coinciding lines and have infinitely many solutions.

Transform both equations to slope-intercept form:

Equation 1:  2(2x+1) = y

                    y = 4x + 2  ⇒ Slope-intercept form of Equation 1.

Equation 2:  y = 2x + 8  

Equation 1: y = 10 − 2x

                    y = − 2x + 10  ⇒ This is the slope-intercept form of Equation 1.

Equation 2:  y = −2x + 7

Since Equations 1 and 2 have the same slope, but different y-intercept, then it means that they are parallel from each other.

Out of all the given four options, Option C seems to be the correct answer, since the given system has varying slopes and y-intercept.  Therefore, the correct answer for Question 1 is Option C:  2(2x+1) = y, y = 2x + 8.

For Question 4, I will not elaborate as thoroughly as in Question 1 since I'll be using the same techniques.

Equation 1:  2x+ 7x + y = 6

Combine like terms:

2x+ 7x + y = 6

9x + y = 6

Subtract 9x from both sides:

9x - 9x + y = - 9x + 6

y = - 9x + 6 ⇒ Slope-intercept form of Equation 1.  

Equation 2: y = 9x + 6

Option A Explanation:

Equations 1 and 2 have different slopes and the same y-intercept. This implies that they will have a point of intersection = one solution. However, they don't have perpendicular lines because their slopes are not negative reciprocal of each other.  Hence, Option A is not a valid answer for  question 4.

Equation 1:  y = 5x + 7

Equation 2:  y = 2x + 8

Option B explanation:

Similar to Option A, Equations 1 and 2 have different slopes and varying y-intercepts. Since they are not parallel from each other, and do not have coinciding lines, then Option B is not a valid answer for  question 4.

Equation 1:  y = x + 4

Equation 2:  2y = 2x + 8

Transform Equation 2 to Slope-intercept form:

Divide both sides by 2 to isolate y:

[tex]\displaytext\mathsf{\frac{2y}{2}\:=\:\frac{2x\:+\:8}{2}}[/tex]

y = x + 4  ⇒ This is the slope-intercept form of Equation 2.  

Option C explanation:

Equations 1 and 2 are equivalent, as they have exactly the same slope and y-intercept. They also have coinciding lines, having infinitely many solutions.  

Equation 1:  7x − y = 10

                    y = 7x - 10  ⇒ This is the slope-intercept form of Equation 1.

Equation 2:  y = 6x + 8

Option D explanation:

Similar to Option B, Equations 1 and 2 have different slopes and varying y-intercepts. Since they are not parallel from each other, and do not have coinciding lines, then Option D is not a valid answer for  question 4.

Select all of the expressions which are equivalent to-4/3p-2/5

What time is it where you guys are at??

The mean, median, and mode of a distribution are __________. A. Measures of central tendency B. Measures of variability C. Types of transformed scores D. Types of deviations Please select the best answer from the choices provided A B C D.

At Keller's Bike Rentals, it costs $36 to rent a bike for 7 hours.
How many hours of bike use does a customer get per dollar

Which of the following is not equivalent to 23 + (-27) - 16-(-32)?
23 – 27 – 16 + 32
o 23 – 27 – 16 – (-32)
O
23 + (-27) + 16 + 32
o
23 + (-27) + (- 16) - (- 32)

A leaky pipe drips 2 fluid ounces of water per hour. How many cups of water does it leak in 2 days? Remember that 8 fluid ounces = 1 cup

1. A scuba diver wants to dive more than 2 1/2, times his previous deepest dive. That means he has to dive at least 80 feet below the surface of the ocean. This dive is represented by the inequality 2 1/2p < -80, where p is the distance below the surface of his previous deepest dive.
The scuba driver's previous deepest dive was ____ feet below the surface of the ocean.
________________________________

Veronica live on a straight road that goes east and west. She starts from a point 5.1 miles west of her home and drives a certain distance to the store the store is more than 3 and 1/2 miles east of her home. let D represent the distance Veronica drove. which inequality represents this situation?
A. -5.1 + d > 3 1/2
B.-5.1 + d > -3 1/2
C.-5.1 + d > 3 1/2
D.- 5.1 + d > -3 1/2

________________________________

Alex needs to represent the statement as an inequality half of a number is more than 1 and 1/3
​

True or false

1: 4h and 4g are like terms: True or false?
2: 4x and 4xy are like terms. True or false?
3: the coefficient is the number by its self. True or false?
4: in the expression x-4+(-5x), the constant is 4. True or false?
5: in the expression x-4+(-5x), the constant is -4. True or false?
6: in the expression x-4+(-5x), the coefficient -5 is . True or false?

You dont need to explain the steps, if you like you may

heeeeeyyyyy someone can aswer plz? Thx

Mother is M years old, and she is 4 times as old as her daughter, her age is x+8/x. how much older is the mother than her daughter, Mary?

PLEASE HELP I REALLY NEED HELP!

What’s the range of = 1 2 ⋅ 2 + 6 + 6

HELP 10 POINTS + BRAINLIEST Determine the equation of the line shown in the graph:
y=0
x=0
y=5
X=5

or
Find the slope of the line
y
=
9
5
x
−
9
5
.

pls help asap MIDSEGMENTS

a 20 pound platter of cookies costs $77. the platter is a mix of peanut butter that costs $4 per pound, sugar that costs $3 per pound, and chocolate chip that’s costs $4.50 per pound. there are two more pounds of sugar cookies than peanut butter. how many pounds of sugar cookies are on the platter?

What are the slope and the y-intercept of the line shown in the graph?

A. y-intercept = 2 and slope = -3
B. y-intercept = 2 and slope = 3
C. y-intercept = 3 and slope = 2
D. y-intercept = 3 and slope = 2

CAN SOMEONE HELP ME PLEASE ASAP!

what is 5 x 1284
plz answer thanks

Cual es el resultado de 12/6?

Singer A and Singer B had the two top-grossing concert tours for a certain year, together generating $334 million in ticket sales. If Singer B took in $26 million less than Singer A, how much did each tour generate?

3/8 rounded to the nearest thousand​

need help with both questions please​

PARALLEL PERPENDICULAR OR NEITHER OR SAME LINE

1) If v2x - 4 = 13x – 8, what is the value of x?
A) 1.
B) 2
4
D) 8

PLS HELP WILL MARK BRAINLIEST! ANSWER W/ SOLUTION

Helppppppppplplppppai

Auntie Anne raked leaves for
more than 10 minutes but less
than 40 minutes. The number
of minutes is a multiple of 5.
The digits add up to 7. For
how long did Anne rake?

pls help asap MIDSEGMENTS

On a coordinate plane, parallelogram P Q R S is shown. Point P is at (negative 2, 5), point Q is at (2, 1), point R is at (1, negative 2), and point S is at (negative 3, 2). In the diagram, SR = 4 StartRoot 2 EndRoot and QR = StartRoot 10 EndRoot. What is the perimeter of parallelogram PQRS?