Question

Identify any solutions to the system given below.

Answer 1

Answer with Step-by-step explanation:

We have to find the solution of the system of equations:

2x + y = 5                

3y = 15 – 6x  which is equivalent to

6x+3y=15            

i.e. 3(2x+y)=15 which is equivalent to: 2x+y=5

both the equation are same hence, there are infinite number of solutions

Now, we check which points satisfies the equation and that will be the solution of the equation.

A.(6, –7)  

Putting x=6 and y=-7, we get

12-7=5

Hence, (6,-7) is a solution.

B.(2, 1)

Putting x=2 and y=1, we get

4+1=5

Hence,(2,1) is also a solution

C.(–2, –9)

Putting x=-2 and y=-9, we get

-4-9=-13≠5

Hence,(-2,-9) is not a solution

D.(–4, 13)

Putting x=-4 and y=13, we get

-8+13=5

Hence, (-4,13) is a solution

Answer 2

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

Explanation:

The given equations are,

$2x+y=5$     ..... (1)

$3y=15-6x$  .... (2)

Simplify the second equation.

$3y+6x=15$

$3(y+2x)=15$

Divide both sides by 3.

$2x+y=5$

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).

$2(6)+(-7)=5$

$5=5$

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

Check for point B(2,1).

$2(2)+(1)=5$

$5=5$

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

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

$2(-2)+(-9)=5$

$-13=5$

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).

$2(-4)+(13)=5$

$5=5$

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.