Asystem of equations has infinetly many solutions. if 2y-4x=6 is one of the equations, which could be the other equation?

Skip to content# Asystem of equations has infinetly many solutions. if 2y-4x=6 is one of the equations, which could be

Mathematics ##
Comments (10) on “Asystem of equations has infinetly many solutions. if 2y-4x=6 is one of the equations, which could be”

### Leave a Reply Cancel reply

Asystem of equations has infinetly many solutions. if 2y-4x=6 is one of the equations, which could be the other equation?

Option C -

Step-by-step explanation:

Given : A system of equations has infinitely many solutions. If is one of the equations.

To find : Which could be the other equation?

Solution :

A system of equations has infinitely many solutions when the two lines representing the equations coincide.

i.e. the two equations are the same or a multiple of each other.

We have given the equation,

Taking 2 common from equation,

or

Take negative both side,

The other equation is

Therefore, option C is correct.

Option C

If 2y – 4x = 6 is one of the equations, then the other equation is -y = -2x - 3

Solution:

Given that,

A system of equations has infinitely many solutions

One of the equation is given as 2y - 4x = 6

We have to find the other equation

A system of equations has infinitely many solutions when the two lines representing the equations coincide. i.e. the two equations are the same or a multiple of each other.

Given one of the equation is 2y - 4x = 6

Take 2 as common term

2(y - 2x) = 6

y - 2x = 3

y = 2x + 3

Multiply the above equation by -1

-y = -2x - 3

This is same as option 3

Thus the other equation is -y = -2x - 3

"infinity many solutions" implies that the two lines coincide.

Example: starting with 2y-4x=6, I multiply every term by 3: 6y-12x=18

These two different-appearing equations are mathematically identical, so graphing both on the same set of axes results in two lines that coincide.

Equation is [tex]-8x+4y-12=0[/tex]

Step-by-step explanation:

An equation is a mathematical statement that two things are equal .

A system of equations is a set of two or more equations consisting of same unknowns.

Two equations [tex]a_1x+b_1y+c_1=0\,,\,a_2x+b_2y+c_2=0[/tex] have unique solution if [tex]\frac{a_1}{a_2}\neq \frac{b_1}{b_2}[/tex]

infinite solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]

no solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]

Here, given: [tex]-4x+2y=6[/tex]

We can write this equation as [tex]-4x+2y-6=0[/tex]

Take another equation as [tex]-8x+4y-12=0[/tex]

Here, [tex]a_1=-4\,,\,a_2=-8\,,\,b_1=2\,,\,b_2=4\,,\,c_1=-6\,,\,c_2=-12[/tex]

[tex]\frac{a_1}{a_2}=\frac{-4}{-8}=\frac{1}{2}\\\frac{b_1}{b_2}=\frac{2}{4}=\frac{1}{2}\\\frac{c_1}{c_2}=\frac{-6}{-12}=\frac{1}{2}[/tex]

such that [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]

The given equation is ⇒⇒⇒ 2y - 4x = 6

∴ 2y = 4x + 6 ⇒ divide all the equation over 2

∴ y = 2x + 3 and it can be written as ⇒⇒⇒ y - 2x = 3

The last equation represents a straight line with a slope = 2 and y-intercept = 3

To construct a system of equations with definitely many solutions and the equation ( 2y-4x=6 ) is one of the equations, the other equation must have the same slope and the same y-intercept.

so, the general solution of the other equation is ⇒ a ( y - 2x ) = 3a

Where a is constant and belongs to R ( All real numbers )

The system of equations which has definitely many solutions is consisting of Coincident lines.

A system of equations has infinitely many solutions when the two lines representing the equations coincide. i.e. the two equations are the same.

2y - 4x = 6

2y = 4x + 6

2y = 2(2x + 3)

y = 2x + 3

-y = -(2x + 3)

-y = -2x - 3

Hence the other equation is -y = -2x - 3

A system of equations may have a minimum of 1 unknown varying upto multiples of unknowns RESPECTIVELY , the same number of simultaneous equations are ALSO required to solve those equations in unknowns

C. -y = -2x -3

The first step I suggest taking, is put 2y-4x = 6 into the same form as your answer choices:

2y - 4x = 6

2y = 4x + 6

y = 2x + 3

Now, we just look at our options choices and see which are the same. If we multiply both sides of y = 2x + 3 by -1, then we get:

–y = –2x – 3

This is the same as C. –y = –2x – 3

A system of equations has infinitely many solutions when the two lines representing the equations coincide. i.e. the two equations are the same or a multiple of each other.

2y - 4x = 6

2y = 4x + 6

2y = 2(2x + 3)

y = 2x + 3

-y = -(2x + 3)

-y = -2x - 3

Hence the other equation is -y = -2x - 3

c

Step-by-step explanation:

correct on edge2020