Respuesta :

Answer: The system of equations have many solutions and the correct options are A,B and D.

Explanation:

The given equations are,

[tex]2x+y=5[/tex]     ..... (1)

[tex]3y=15-6x[/tex]  .... (2)

Simplify the second equation.

[tex]3y+6x=15[/tex]

[tex]3(y+2x)=15[/tex]

Divide both sides by 3.

[tex]2x+y=5[/tex]

It is same as equation (1). Since equation (1) and (2) are same, therefore all the points lies on the line or which satisfies the equation are the solution of the given system of equations.

Test the points whether the point lies on the line or not.

Check for point A(6,-7).

[tex]2(6)+(-7)=5[/tex]

[tex]5=5[/tex]

LHS and RHS are equal, therefore the point A is the solution of the system of equations.

Check for point B(2,1).

[tex]2(2)+(1)=5[/tex]

[tex]5=5[/tex]

LHS and RHS are equal, therefore the point B is the solution of the system of equations.

Check for point C(-2,-9).

[tex]2(-2)+(-9)=5[/tex]

[tex]-13=5[/tex]

LHS and RHS are not equal, therefore the point C is not the solution of the system of equations.

Check for point D(-4,13).

[tex]2(-4)+(13)=5[/tex]

[tex]5=5[/tex]

LHS and RHS are equal, therefore the point D is the solution of the system of equations.

Therefore the options A,B and D are correct.

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The points (6, –7), (2, 1), and (–4, 13) satisfies the equation and hence, will be the solution of the equation. The correct solution for this system is A, B, and D.

Given:

The given system of linear equations is,

[tex]2x + y = 5\\3y = 15 - 6x[/tex]

Equate the y coefficient of the equations and write them as,

[tex]6x + 3y = 15\\6x+3y = 15[/tex]

The given system of equation is the same equation and hence, will have infinite solutions.

Now, the solution of equation from the given options can be found by putting each point in the equation and checking for its satisfaction of the equation.

So, try All the points given. Point A(6,-7) Where x=6, y=-7

Put in equation.

[tex]-7+2(6)=5\\-7+12=5\\5=5[/tex]

Hence LHS=RHS

Point B(2,1), Where x=2, y=1

Put in equation.

[tex]1+2(2)=5\\1+4=5\\5= 5[/tex]

Hence, LHS= RHS

Point C(-2,-9), Where x=-2, y=-9

Put in equation.

[tex]-9+2(-2)=5\\-9-4=5\\-13\neq 5[/tex]

Hence LHS[tex]\neq[/tex]RHS

Point D(-4,13)

Where x=-4, y=13

Put in equation.

[tex]13+2(-4)=5\\13-8=5\\5=5[/tex]

Hence, LHS= RHS

Therefore, points (6, –7), (2, 1), and (–4, 13) satisfies the equation and hence. will be the solution of the equation.

Learn more about coordinate geometry here

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