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

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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)

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