Use the substitution method to solve the system of equations. choose the correct ordered pair. x + y = 11 –x = –y – 9 a.(9, 2) b.(10, 1) c.(11, 0) d.(8, 3)

Step-by-step explanation:

B.(10,1)

Statement 1 : True

Statement 2: False

Statement 3: False

Statement 4:True

Statement 5:False

Statement 6:True

Step-by-step explanation:

Given :

To Find: Which statements about the system are true?

Solution:

Slope intercept form:

where m is the slope

Convert the given equations in slope intercept form

Equation 1:

 --A

On comparing with general form

Slope = m =

Equation 2:

 --B

On comparing with general form

Slope = m = 1

Substitute the value of x form B in A

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

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 and slope of line 2 is 1

Since the slopes are not same

So, statement 3 is false.

Equation 1:

To find y intercept substitute x =0

Equation 2:

To find y intercept substitute x =0

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)