Question

Which graph shows the following system of equations and its solutions? -0.1x-0.3y=1.2 and 0.2x-0.5y=2

Answer 1

Option b is the correct answer as both the equations are true for given solution.

Explanation:

Given equations are:

-0.1x-0.3y=1.2

0.2x-0.5y=2

We can observe each graph and find the point that is the solution and put the point in the equations to know if that point is the solution

For option A:

(0,4)

Putting x=0 and y = 4 in both equations

`-0.1(0)-0.3(4)=1.2\\0-1.2 =1.2\\-1.2 \\eq 1.2\\0.2(0)-0.5(4)=2\\0-2 = 2\\-2 \\eq 2`

This is not the correct answer as both equations are not true with this solution

For Option B:

(0,-4)

Putting x = 0 and y = -4 in both equations

`-0.1(0)-0.3(-4)=1.2\\0+1.2 = 1.2\\1.2 = 1.2\\0.2x-0.5y=2\\0.2(0)-0.5(-4) = 2\\2 = 2`

Both equations are true for (0,-4) hence it is the solution of the system.

For Option C:

(4,0)

`-0.1(4)-0.3(0)=1.2\\-0.4-0 = 1.2\\-0.4 \\eq 1.2\\0.2x-0.5y=2\\0.2(4)-0.5(0) = 2\\0.8 \\eq 2`

Not true for both equations

Hence,

Option b is the correct answer.