Mathematics, 14.04.2020 23:29 brooke012002

6Of
Consider the system of linear equations.
2y = x + 10
3y = 3x + 15
Which statements about the system are true? Check all
that apply.
The system has one solution.
The system graphs parallel lines.
Both lines have the same slope.
Both lines have the same y-intercept.
The equations graph the same line.
The solution is the intersection of the 2 lines.

6Of Consider the system of linear equations. 2y = x + 10 3y = 3x + 15 Which statements about the sys

Answers: 2

Show answers

Answers

Answer from: deena7

Statement 1 : True

Statement 2: False

Statement 3: False

Statement 4:True

Statement 5:False

Statement 6:True

Step-by-step explanation:

Given : 2y = x + 10

3y = 3x + 15

To Find: Which statements about the system are true?

Solution:

Slope intercept form: y =mx+c

where m is the slope

Convert the given equations in slope intercept form

Equation 1: 2y = x + 10

$y = \frac{x}{2}+\frac{10}{2}$

$y = \frac{x}{2} +5$ --A

On comparing with general form

Slope = m = $\frac{1}{2}$

Equation 2: 3y = 3x + 15

$y = \frac{3}{3}x + \frac{15}{3}$

y = x +5 --B

On comparing with general form

Slope = m = 1

Substitute the value of x form B in A

$y = \frac{y-5}{2} +5$

$y-5 = \frac{y-5}{2}$

2y-10 = y-5

y=5

Substitute the value of y in B to get value of x

5 = x +5

x=0

Thus the solution is (0,5)

Thus The system has one solution.

So, Statement 1 is true

Since the slopes of the given lines are not same so the lines are not parallel

Thus the statement 2 is false.

Slope of line 1 is $\frac{1}{2}$ and slope of line 2 is 1

Since the slopes are not same

So, statement 3 is false.

Equation 1: 2y = x + 10

To find y intercept substitute x =0

2y = 0 + 10

$y =\frac{10}{2}$

y =5

Equation 2: 3y = 3x + 15

To find y intercept substitute x =0

3y = 3(0) + 15

$y =\frac{15}{3}$

y =5

So,statement 4 is true Both lines have the same y-intercept.

Statement 5: The equations graph the same line.

Statement 5 is false (refer the attached graph)

Statement 6 is true The solution is the intersection of the 2 lines (refer the attached graph)

Consider the system of linear equations. 2y = x + 10 3y = 3x + 15 which statements about the system

Answer from: jeffcarpenter

Statement 1 : True

Statement 2: False

Statement 3: False

Statement 4:True

Statement 5:False

Statement 6:True

Step-by-step explanation:

Given : 2y = x + 10

3y = 3x + 15

To Find: Which statements about the system are true?

Solution:

Slope intercept form: y =mx+c

where m is the slope

Convert the given equations in slope intercept form

Equation 1: 2y = x + 10

$y = \frac{x}{2}+\frac{10}{2}$

$y = \frac{x}{2} +5$ --A

On comparing with general form

Slope = m = $\frac{1}{2}$

Equation 2: 3y = 3x + 15

$y = \frac{3}{3}x + \frac{15}{3}$

y = x +5 --B

On comparing with general form

Slope = m = 1

Substitute the value of x form B in A

$y = \frac{y-5}{2} +5$

$y-5 = \frac{y-5}{2}$

2y-10 = y-5

y=5

Substitute the value of y in B to get value of x

5 = x +5

x=0

Thus the solution is (0,5)

Thus The system has one solution.

So, Statement 1 is true

Since the slopes of the given lines are not same so the lines are not parallel

Thus the statement 2 is false.

Slope of line 1 is $\frac{1}{2}$ and slope of line 2 is 1

Since the slopes are not same

So, statement 3 is false.

Equation 1: 2y = x + 10

To find y intercept substitute x =0

2y = 0 + 10

$y =\frac{10}{2}$

y =5

Equation 2: 3y = 3x + 15

To find y intercept substitute x =0

3y = 3(0) + 15

$y =\frac{15}{3}$

y =5

So,statement 4 is true Both lines have the same y-intercept.

Statement 5: The equations graph the same line.

Statement 5 is false (refer the attached graph)

Statement 6 is true The solution is the intersection of the 2 lines (refer the attached graph)

Another question on Mathematics

Mathematics, 21.06.2019 18:00

10 ! a train starts from grand city and travels toward belleville 388 miles away. at the same time, a train starts from belleville and runs at the rate of 47 miles per hour toward grand city. they pass each other 4 hours later. find the rate of the train from grand city.

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

Which number line represents the solution set for the inequality -1/2x> 24?

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

If you are dealt 4 cards from a shuffled deck of 52? cards, find the probability that all 4 cards are diamondsdiamonds.

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

If u good at math hit me up on insta or sum @basic_jaiden or @ and