Mathematics: What is the solution to this system of linear equation

What is the solution to this system of linear, №13353190, 01.08.2020 05:31

Mathematics

Michiko claims that to solve the system of linear equations 15 x + 8 y = 1 and 21 x + 4 y = negative 13, instead of multiplying the second equation by –2 and then adding the equations, she could multiply the second equation by 2 and then subtract the second equation from the first equation. Which statement is correct? Michiko is right for this system of linear equations, but her method will not work for other systems of linear equations. Michiko is right for this system of linear equations, and her method will also work for other systems of linear

Step-by-step answer

P Answered by Master

6

Michiko is right for this system of linear equations, and her method will also work for other systems of linear equations.

Mathematics

Michiko claims that to solve the system of linear equations 15 x + 8 y = 1 and 21 x + 4 y = negative 13, instead of multiplying the second equation by –2 and then adding the equations, she could multiply the second equation by 2 and then subtract the second equation from the first equation. Which statement is correct? Michiko is right for this system of linear equations, but her method will not work for other systems of linear equations. Michiko is right for this system of linear equations, and her method will also work for other systems of linear

Step-by-step answer

P Answered by PhD

Answer: a. Michiko is right for this system of linear equations, but her method will not work for other systems of linear equations.

Explanation:
Given:
15 x + 8 y = 1;
21 x + 4 y = - 13.
Multiplying the second equation by –2 and then adding the equations
15x + 8y = 1;
-42x - 8y = 26.
Subtract the second equation from the first:
-27x + 0 = 27,
so x = -1 and y= 2.
So we choose: " Michiko is right for this system of linear equations, and her method will also work for other systems of linear equations."

Mathematics

6) (after 2.3) Consider the infinite system of linear equations in two variables given by ax + by = 0 where (a, b) moves along the unit circle in the plane. (a) How many solutions does this system have? (b) What is the smallest number of equations in the above system that have the same solution set? Write down two separate such linear systems, in vector form. (c) What happens to the infinite linear system if you add the equation 0x + 0y = 0 to it? (d) What happens to the infinite linear system if by accident one of the equations was recorded as

Step-by-step answer

P Answered by Specialist

Step-by-step explanation:

Given infinite system of linear equations is ax + by = 0

when (a,b) moves along unit circle in plane.

a) system having unique system (0, 0)

Since two of equation in thus system will be

$1.x+0.y=0\\x=0$

and

$0.x+1.y=0\\y=0$

It is clear that x = 0, y= 0 is the only solution

b) Linear independent solution in this system gives some set of solutions

$1.x+0.y=0\\\x=0$

and

$0.x+1.y=0\\y=0$

Vector form is

$\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] =I$

c) for this equation if add 0x +0y = 0 to system , Nothing will change

Because [0,0] satisfies that equation

d) If one of the equation is ax + by = 0.00001

where 0.00001 is small positive number

so, the system will be inconsistent

Therefore, the system will have no solution.

Mathematics

Match the following items 1)linear equation (specific) 2)graph of system of linear equations with no solution 3)slope of a vertical line 4)graph of linear inequality 5)slope of a horizontal line 6)system of linear equations a)2x + 3y = 8 b)2x + y = 7 and 3x - 4y = 8 c)0 d)no slope e)parallel lines f)half-plane

Step-by-step answer

P Answered by PhD

2

The right answer for the question that is being asked and shown above is that:

1)linear equation (specific) => A)2x + 3y = 8
2)graph of system of linear equations with no solution => E)parallel lines
3)slope of a vertical line => D)no slope
4)graph of linear inequality => F)half-plane
5)slope of a horizontal line => C)0
6)system of linear equations => B)2x + y = 7 and 3x - 4y = 8

Mathematics

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are

Step-by-step answer

P Answered by Master

1

A. Yes, overdetermined systems can be consistent.

As, the system of equations below is consistent because it has a solution

$x_{1}=2$ , $x_{2}=4$ , $x_{1}+x_{2}=6$ .

Step-by-step explanation:

We have,

'Over-determined system is a system of linear equations, in which there are more equations than unknowns'.

For e.g. Let us consider the system,

2x - 3y = 1

3x - 2y = 4

x - y = 1

Plotting these equations, we see from the graph below that,

The only intersection point is (2,1). Thus, x= 2 and y= 1 is the solution of this system.

Thus, over-determined system can be consistent.

According to the options,

Option C is not correct as,

$x_{1}=2$ , $x_{2}=4$ implies $x_{1}+x_{2}=2+4=6\neq 8$ .

Hence, option A is correct.

Mathematics

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are

Step-by-step answer

P Answered by Specialist

1

A. Yes, overdetermined systems can be consistent.

As, the system of equations below is consistent because it has a solution

$x_{1}=2$ , $x_{2}=4$ , $x_{1}+x_{2}=6$ .

Step-by-step explanation:

We have,

'Over-determined system is a system of linear equations, in which there are more equations than unknowns'.

For e.g. Let us consider the system,

2x - 3y = 1

3x - 2y = 4

x - y = 1

Plotting these equations, we see from the graph below that,

The only intersection point is (2,1). Thus, x= 2 and y= 1 is the solution of this system.

Thus, over-determined system can be consistent.

According to the options,

Option C is not correct as,

$x_{1}=2$ , $x_{2}=4$ implies $x_{1}+x_{2}=2+4=6\neq 8$ .

Hence, option A is correct.

Mathematics

Which of the following terms best describes a group of equations in which at least one equation is nonlinear, all of the equations have the same variables, and all of the equations are used together to solve a problem? a. system of linear inequalities b. system of linear equations c. system of nonlinear equations d. system of nonlinear inequalities

Step-by-step answer

P Answered by Specialist

103

C. System of non-linear equations

Explanation:
A system is defined as a group of equations/inequalities all having the same variables and are solved together.

Since we are looking for a system of EQUATIONS, we can exclude options A and D since they refer to inequalities

Now, we are left with options B and C:
1- Option B:
This options refers to a system of linear equations. This means that all equations in the system are linear. Therefore, this option is incorrect

2- Option C:
This option refers to a system of non-linear equations. This means that at least one of the equations in the systems is non-linear. This fits the description given in the question. Therefore, this is the correct option

Hope this helps :)

Mathematics

Asystem of two linear equations is shown. 5x + 2y = –4 5x + 2y = 1 which statement is true regarding the solution to this system of linear equations? a.the system has no solution. b.the system has one unique solution at (5, 2). c. the system has one unique solution at (–4, 1). d. the system has an infinite number of solutions.

Step-by-step answer

P Answered by PhD

4

We need to find which of the given statements are true.

The system of linear equations has no solutions.

First let us find what type of solution does the system have

The equations are

5x+2y=-4

5x+2y=1

So,

$\dfrac{a_1}{a_2}=\dfrac{5}{5}=1$

$\dfrac{b_1}{b_2}=\dfrac{2}{2}=1$

$\dfrac{c_1}{c_2}=\dfrac{-4}{1}=-4$

So,

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}$

This means the two lines do not intersect and are parallel.

Hence, the system of linear equations has no solutions.

Learn more:

link

Mathematics

Systems of Linear Equations What are the different ways to solve a system of linear equations? When do you get an answer to a system of linear equations that has one solution, no solution and infinitely many solutions? Solve each of the following systems by graphing. y = -x – 7 y = 4/3 x – 7 y = -3x – 5 y = x + 3 y = -2x + 5 y = 1/3 x – 2 3x + 2y = 2 x + 2y = -2 x + 3y = -9 2x – y = -4 x – 2y = 2 -x + 4y = -8 5x + y = -2 x + y = 2

Step-by-step answer

P Answered by PhD

2

Different ways to solve a system of linear equations:

isolate one variable in one equation and replace it in the other equationmultiply/divide one equation by a constant and then add/subtract it to the other one, so that only one variable remainsgraph the equation and look at the intersection point

If you graph the system:

there is only one solution if the lines intersects at only one pointthere is no solution if the lines don't intersect each other (they are parallel)there are infinitely many solutions if the lines overlap each other (they are the same equation multiplied by some constant)

Step-by-step explanation:

1st system

y = -x – 7

y = 4/3 x – 7

solution: x= 0, y = 7

2nd system

y = -3x – 5

y = x + 3

solution: x = -2, y = 1

3rd system

y = -2x + 5

y = 1/3 x – 2

solution: x = 3, y = -1

4th system

3x + 2y = 2

x + 2y = -2

solution: x = 2, y = -2

5th system

x + 3y = -9

2x – y = -4

solution: x = -3, y = -2

6th system

x – 2y = 2

-x + 4y = -8

solution: x = -4, y = -3

7th system

5x + y = -2

x + y = 2

solution: x = -1, y = -3

Systems of Linear Equations What are the different ways to solve a system of linear equations? When

Mathematics

6) (after 2.3) Consider the infinite system of linear equations in two variables given by ax + by = 0 where (a, b) moves along the unit circle in the plane. (a) How many solutions does this system have? (b) What is the smallest number of equations in the above system that have the same solution set? Write down two separate such linear systems, in vector form. (c) What happens to the infinite linear system if you add the equation 0x + 0y = 0 to it? (d) What happens to the infinite linear system if by accident one of the equations was recorded as

Step-by-step answer

P Answered by Master

Step-by-step explanation:

Given infinite system of linear equations is ax + by = 0

when (a,b) moves along unit circle in plane.

a) system having unique system (0, 0)

Since two of equation in thus system will be

$1.x+0.y=0\\x=0$

and

$0.x+1.y=0\\y=0$

It is clear that x = 0, y= 0 is the only solution

b) Linear independent solution in this system gives some set of solutions

$1.x+0.y=0\\\x=0$

and

$0.x+1.y=0\\y=0$

Vector form is

$\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] =I$

c) for this equation if add 0x +0y = 0 to system , Nothing will change

Because [0,0] satisfies that equation

d) If one of the equation is ax + by = 0.00001

where 0.00001 is small positive number

so, the system will be inconsistent

Therefore, the system will have no solution.

What is the solution to this system of linear equation

Faq

Try asking the Studen AI a question.