a system of two equations has no solution if, №10675458, 23.10.2020 07:17

Mathematics

Is the following statement correct? explain. a system of two equations has no solution if the graphs of the two equations are coincident lines.

Step-by-step answer

P Answered by Master

4

The answer is NO.

Step-by-step explanation: The given statement is -

If the graph of two equations are coincident lines, then that system of equations will have no solution.

We are to check whether the above statement is correct or not.

Any two equations having graphs as coincident lines are of the form -

$ax+by=c,\\\\dax+dby=dc,\\\\\textup{where}~~d\neq 1.$

If we take d = 1, then both the equations will be same.

Now, subtracting the second equation from first, we have

$a(1-d)x+b(1-d)y=c(1-d)\\\\\Rightarrow ax+by=c,~\textup{since}~d\neq 1,~\textup{so}~1-d\neq 0.$

Again, we will get the first equation, which is linear in two unknown variables. So, the system will have infinite number of solutions, which consists of the points lying on the line.

For example, see the attached figure, the graphs of following two equations is drawn and they are coincident. Also, the result is again the same straight line which has infinite number of points on it. These points makes the solution for the following system.

$2x+5y=10,\\\\6x+15y=30.$

Thus, the given statement is not correct.

Mathematics

Is the following statement correct? explain. a system of two equations has no solution if the graphs of the two equations are coincident lines.

Step-by-step answer

P Answered by Master

4

The answer is NO.

Step-by-step explanation: The given statement is -

If the graph of two equations are coincident lines, then that system of equations will have no solution.

We are to check whether the above statement is correct or not.

Any two equations having graphs as coincident lines are of the form -

$ax+by=c,\\\\dax+dby=dc,\\\\\textup{where}~~d\neq 1.$

If we take d = 1, then both the equations will be same.

Now, subtracting the second equation from first, we have

$a(1-d)x+b(1-d)y=c(1-d)\\\\\Rightarrow ax+by=c,~\textup{since}~d\neq 1,~\textup{so}~1-d\neq 0.$

Again, we will get the first equation, which is linear in two unknown variables. So, the system will have infinite number of solutions, which consists of the points lying on the line.

For example, see the attached figure, the graphs of following two equations is drawn and they are coincident. Also, the result is again the same straight line which has infinite number of points on it. These points makes the solution for the following system.

$2x+5y=10,\\\\6x+15y=30.$

Thus, the given statement is not correct.

Mathematics

Two roads are represented by lines on a coordinate grid. two points on each of the roads are shown in the tables. (a) write the equation for road 1 in slope-intercept form. (b) write the equation for road 2 in point-slope form and then in slope-intercept form. (c) is the system of equations consistent independent, coincident, or inconsistent? explain (d) if the two roads intersect, what are the coordinates of the point of intersection? use the substitution method and show your work.

Step-by-step answer

P Answered by PhD

4

(A) y - 7 = 2(x -2)

(B) y = -x + 6; y - 5 = -1(x + 1)

(C) Consistent independent

(D) (1, 5)

Step-by-step explanation:

(A) Road 1

(a) Slope

The point-slope formula for a straight line is

y₂ - y₁ = m(x₂ - x₁) Insert the points

3 - 7 = m(0 - 2)

-4 = m(-2) Divide each side by -2

m = -4/(-2) Divide numerator and denominator by-2,

m = 2

=====

(b) y-intercept

y₂ - y₁ = m(x₂ - x₁)

y₂ - 7 = 2(x₂ -2)

y - 7 = 2(x -2)

===============

(B) Road 2

(a) Slope

y = mx + b

Choose point (3,3)

m = (3 - 5)/(3 - 1)

m = -2/2

m = -1

=====

(b) y-intercept

y = mx +b

Choose point (3,3).

3 = -3 + b Add 3 to each side

b = 6

=====

(c) Equation of line (point-slope form)

y = mx + b

y = -x + 6

=====

(d) Equation of line (slope-intercept form)

y - 5 = -1(x - 1)

===============

(C) Consistency

The two roads intersect.

There is only one point of intersection, so this is a consistent, independent system of equations

===============

(D) Point of intersection

(1) y - 7 = 2(x - 2)

(2) y = -x + 6 Substitute (2) into (1)

-x + 6 – 7 = 2(x – 2) Remove parentheses

-x - 1 = 2x – 4 Add 4 to each side

-x +3 = 2x Add x to each side

3 = 3x Divide each side by 3

x = 1 Substitute into 2

=====

y = -1 + 6

y = 5

The point of intersection is (1, 5).

Mathematics

Two roads are represented by lines on a coordinate grid. two points on each of the roads are shown in the tables. (a) write the equation for road 1 in slope-intercept form. (b) write the equation for road 2 in point-slope form and then in slope-intercept form. (c) is the system of equations consistent independent, coincident, or inconsistent? explain (d) if the two roads intersect, what are the coordinates of the point of intersection? use the substitution method and show your work.

Step-by-step answer

P Answered by PhD

4

(A) y - 7 = 2(x -2)

(B) y = -x + 6; y - 5 = -1(x + 1)

(C) Consistent independent

(D) (1, 5)

Step-by-step explanation:

(A) Road 1

(a) Slope

The point-slope formula for a straight line is

y₂ - y₁ = m(x₂ - x₁) Insert the points

3 - 7 = m(0 - 2)

-4 = m(-2) Divide each side by -2

m = -4/(-2) Divide numerator and denominator by-2,

m = 2

=====

(b) y-intercept

y₂ - y₁ = m(x₂ - x₁)

y₂ - 7 = 2(x₂ -2)

y - 7 = 2(x -2)

===============

(B) Road 2

(a) Slope

y = mx + b

Choose point (3,3)

m = (3 - 5)/(3 - 1)

m = -2/2

m = -1

=====

(b) y-intercept

y = mx +b

Choose point (3,3).

3 = -3 + b Add 3 to each side

b = 6

=====

(c) Equation of line (point-slope form)

y = mx + b

y = -x + 6

=====

(d) Equation of line (slope-intercept form)

y - 5 = -1(x - 1)

===============

(C) Consistency

The two roads intersect.

There is only one point of intersection, so this is a consistent, independent system of equations

===============

(D) Point of intersection

(1) y - 7 = 2(x - 2)

(2) y = -x + 6 Substitute (2) into (1)

-x + 6 – 7 = 2(x – 2) Remove parentheses

-x - 1 = 2x – 4 Add 4 to each side

-x +3 = 2x Add x to each side

3 = 3x Divide each side by 3

x = 1 Substitute into 2

=====

y = -1 + 6

y = 5

The point of intersection is (1, 5).

Physics

(3 points) A disk is spinning freely with angular speed 6.0 rad/s when a second identical disk, initially not spinning, is dropped on it so that their axes coincide. In a short time the two disks are co-rotating. a) Sketch the initial situation and the consequential situation. b) What is the angular speed of the new system? c) If a third such disk is dropped on the first two, find the final angular speed of the system.

Step-by-step answer

P Answered by Master

a) The sketch is attached.

b) The angular speed of the new system is 3 rad/s

c) The angular speed of the new system is 2 rad/s

Explanation:

b) The angular speed of the system is:

$I_{i} w_{i} =I_{f} w_{f}$

Where

Ii = I

If = I + I

wi = 6 rad/s

Replacing:

$I*6=(I+I)w_{f} \\w_{f} =\frac{6I}{2I} =3rad/s$

c) If a third disk is dropped, the angular speed is:

$I*6=(I+I+I)w_{f} \\w_{f} =\frac{6I}{3I} =2rad/s$

(3 points) A disk is spinning freely with angular speed 6.0 rad/s when a second identical disk, init

Mathematics

If a graph of a system of two equations shows two lines that coincide on a coordinate plane, how many solutions does the system have? a) no solution b) exactly one solution c) infinitely many solutions d) cannot be determined from the graph

Step-by-step answer

P Answered by Specialist

10

If a graph of a system of two equations shows two lines that coincide on a coordinate plan there would be C.)Infinitely many solutions

I hope this helps, have a great day.

Physics

(3 points) A disk is spinning freely with angular speed 6.0 rad/s when a second identical disk, initially not spinning, is dropped on it so that their axes coincide. In a short time the two disks are co-rotating. a) Sketch the initial situation and the consequential situation. b) What is the angular speed of the new system? c) If a third such disk is dropped on the first two, find the final angular speed of the system.

Step-by-step answer

P Answered by Specialist

a) The sketch is attached.

b) The angular speed of the new system is 3 rad/s

c) The angular speed of the new system is 2 rad/s

Explanation:

b) The angular speed of the system is:

$I_{i} w_{i} =I_{f} w_{f}$

Where

Ii = I

If = I + I

wi = 6 rad/s

Replacing:

$I*6=(I+I)w_{f} \\w_{f} =\frac{6I}{2I} =3rad/s$

c) If a third disk is dropped, the angular speed is:

$I*6=(I+I+I)w_{f} \\w_{f} =\frac{6I}{3I} =2rad/s$

Mathematics

If a graph of a system of two equations shows two lines that coincide on a coordinate plane, how many solutions does the system have? a) no solution b) exactly one solution c) infinitely many solutions d) cannot be determined from the graph

Step-by-step answer

P Answered by Specialist

10

If a graph of a system of two equations shows two lines that coincide on a coordinate plan there would be C.)Infinitely many solutions

I hope this helps, have a great day.

Mathematics

2x + 3y = -17 is one equation in a coincidental system of two linear equations. the other equation is _ y = _ x – 102. find the other two variables for the second equations.

Step-by-step answer

P Answered by Master

12

Rewrite the first equation: 3y=-2x-17. The equations are coincidental and -17 is one sixth of -102 so the other coefficients need to be multiplied by 6: 18y=-12x-102.

Mathematics

If a system of two linear equations has no solutions, which of the following statements describes the graph of the two corresponding lines in the xy-plane? a. The lines are coinciding b. The lines intersect at only one point c. The lines are parallel d. The lines are perpendicular Explain why you picked your

Step-by-step answer

P Answered by PhD

3 because it is the best

a system of two equations has no solution if the graphs of the two equations are coincident line .

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