Question

Is the system of equations is consistent, consistent and coincident, or inconsistent? y=−x−13y=−3x+2

Answer 1

its inconsistent .......

Answer 2

The System of Equation is Consistent.

Explanation:

Given: System of equations y = -x - 13 and y = -3x + 2

To find: System of equation is consistent or inconsistent

System of equation is consistent if it has a unique solution or infinitely many solution and it is in consistent if it has no solution.

So we check if given system of equation has unique solution or infinitely many solution or no solution by checking their ratio.

Rewrite the system of equation,

x + y +13 = 0 and 3x + y - 2 = 0

`a_1=1\:,\:b_1=1\:,\:c_1=13\:and\:a_2=3\:,\:b_2=1\:,\:c_2=-2`

Now,

`(a_1)/(a_2)=(1)/(3)`

`(b_1)/(b_2)=(1)/(1)`

`(c_1)/(c_2)=(13)/(-2)`

Since,
`(a_1)/(a_2)\\eq(b_1)/(b_2)`

Thus, System of equation has unique solution.

Therefore, The System of Equation is Consistent.